{"id":5451,"date":"2025-10-01T08:35:40","date_gmt":"2025-10-01T08:35:40","guid":{"rendered":"https:\/\/sigfigcalculator.io\/?page_id=5451"},"modified":"2025-10-01T08:35:40","modified_gmt":"2025-10-01T08:35:40","slug":"decimal-to-radical-calculator","status":"publish","type":"page","link":"https:\/\/sigfigcalculator.io\/pt\/decimal-to-radical-calculator\/","title":{"rendered":"Decimal to Radical Calculator \u2013 Convert Numbers Easily"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"5451\" class=\"elementor elementor-5451\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6ccb5747 e-con-full e-flex e-con e-parent\" data-id=\"6ccb5747\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-18fd9c8f elementor-widget elementor-widget-shortcode\" data-id=\"18fd9c8f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><!-- START: Decimal to Radical Calculator Hero Block (v2 - Fixed Input & Auto-Scaling Output) -->\r\n<div class=\"dtr-container\">\r\n    <!-- \r\n        Designer & Developer Notes (v2 - Decimal\/Radical):\r\n        Theme: Architectural Matte & Soft Focus\r\n        CRITICAL UPGRADES IMPLEMENTED:\r\n        1. LOCKED INPUT WIDTH: The input deck is now a fixed 340px on desktops for a stable,\r\n           predictable user interaction zone. It gracefully becomes full-width on smaller screens.\r\n        2. AUTO-SCALING OUTPUT: A new JavaScript function intelligently detects when the output number\r\n           is too long to fit and automatically applies a smaller font size. This prevents text from\r\n           ever being cut off and ensures a flawless presentation for any result.\r\n        3. ROBUST RESPONSIVE GRID: The CSS Grid has been re-engineered to accommodate the new\r\n           fixed\/fluid column behavior across all specified breakpoints.\r\n        4. WP-PROOF & PRODUCTION-READY: All class prefixes and high-specificity selectors are maintained.\r\n    -->\r\n    <style>\r\n        \/* FONT IMPORT *\/\r\n        @import url('https:\/\/fonts.googleapis.com\/css2?family=Satoshi:wght@400;700&display=swap');\r\n        @import url('https:\/\/fonts.googleapis.com\/css2?family=Source+Serif+4:opsz,wght@8..60,600&display=swap');\r\n\r\n        \/* CSS VARIABLES *\/\r\n        .dtr-container {\r\n            --dtr-bg-start: #ffffff;\r\n            --dtr-bg-end: #ffffff;\r\n            --dtr-panel: #FFFFFF;\r\n            --dtr-accent: #192A51;\r\n            --dtr-text-primary: #192A51;\r\n            --dtr-text-secondary: #79829B;\r\n            --dtr-input-bg: #F4F6FB;\r\n            --dtr-border: #E1E6F0;\r\n            --dtr-shadow: rgba(25, 42, 81, 0.1);\r\n            --dtr-font-primary: 'Satoshi', 'Inter', sans-serif;\r\n            --dtr-font-serif: 'Source Serif 4', serif;\r\n            --dtr-radius: 20px;\r\n        }\r\n\r\n        \/* --- BULLETPROOF BASE & HERO LAYOUT --- *\/\r\n        .dtr-container { font-family: var(--dtr-font-primary); background: linear-gradient(135deg, var(--dtr-bg-start) 0%, var(--dtr-bg-end) 100%); padding: 120px 0; width: 100%; position: relative; box-sizing: border-box; }\r\n        .dtr-container *, .dtr-container *::before, .dtr-container *::after { box-sizing: inherit; }\r\n        .dtr-container h1, .dtr-container p { margin: 0; padding: 0; font: inherit; }\r\n        .dtr-container button, .dtr-container input { margin: 0; font-family: inherit; -webkit-appearance: none; -moz-appearance: none; appearance: none; }\r\n        .dtr-container .dtr-hero-wrapper { max-width: 1160px; margin: 0 auto; padding: 0 40px; display: grid; justify-items: center; gap: 60px; }\r\n        .dtr-container .dtr-hero-content { text-align: center; opacity: 0; transform: translateY(20px); transition: opacity 0.6s ease-out, transform 0.6s ease-out; }\r\n        .dtr-container .dtr-hero-content--loaded { opacity: 1; transform: translateY(0); }\r\n        .dtr-container .dtr-hero-content__title { font-size: 3.8rem; font-weight: 700; line-height: 1.15; color: var(--dtr-text-primary); margin-bottom: 20px; }\r\n        .dtr-container .dtr-hero-content__highlight { color: var(--dtr-accent); }\r\n        .dtr-container .dtr-hero-content__subtitle { font-size: 1.2rem; color: var(--dtr-text-secondary); line-height: 1.6; margin: 0 auto; max-width: 720px; }\r\n\r\n        \/* --- ARCHITECTURAL MATTE CARD --- *\/\r\n        .dtr-container .dtr-card { width: 100%; background: var(--dtr-panel); border-radius: var(--dtr-radius); box-shadow: 0 25px 50px -12px var(--dtr-shadow); padding: 50px; opacity: 0; transform: translateY(20px); transition: opacity 0.6s ease-out 0.15s, transform 0.6s ease-out 0.15s; }\r\n        .dtr-container .dtr-card--loaded { opacity: 1; transform: translateY(0); }\r\n        \r\n        \/* NEW: Grid with fixed input column *\/\r\n        .dtr-container .dtr-card__grid { display: grid; grid-template-columns: 340px 1fr; gap: 50px; }\r\n\r\n        \/* Left: Input Deck (Fixed Width) *\/\r\n        .dtr-container .dtr-card__input-deck { display: flex; flex-direction: column; justify-content: center; }\r\n        .dtr-container .dtr-section__label { font-size: 1rem; font-weight: 700; color: var(--dtr-text-secondary); margin-bottom: 16px; display: block; }\r\n        .dtr-container .dtr__input { width: 100%; background-color: var(--dtr-input-bg); border: 2px solid var(--dtr-border); border-radius: 12px; padding: 20px; font-size: 2.5rem; color: var(--dtr-text-primary); font-weight: 700; transition: all 0.2s ease; }\r\n        .dtr-container .dtr__input:focus { outline: none; border-color: var(--dtr-accent); box-shadow: 0 0 0 4px rgba(25, 42, 81, 0.1); }\r\n        \r\n        \/* Right: Results Dashboard (Fluid Width) *\/\r\n        .dtr-container .dtr-card__results-dashboard { display: flex; flex-direction: column; justify-content: space-between; min-width: 0; \/* Prevents overflow on flex child *\/ }\r\n        .dtr-container .dtr-primary-result { display: flex; align-items: center; justify-content: center; font-family: var(--dtr-font-serif); font-size: 25px; font-weight: 600; color: var(--dtr-text-primary); text-align: center; min-height: 120px; transition: font-size 0.3s ease-out; }\r\n        \r\n        \/* NEW: Auto-scaling font size class *\/\r\n        .dtr-container .dtr-primary-result--shrunk { font-size: 25px; }\r\n        \r\n        .dtr-container .dtr-primary-result__coeff { margin-right: 0.2em; white-space: nowrap; overflow: hidden; text-overflow: ellipsis; }\r\n        .dtr-container .dtr-primary-result__radicand { border-top: 3px solid var(--dtr-accent); padding: 0 0.4em; white-space: nowrap; overflow: hidden; text-overflow: ellipsis; }\r\n        .dtr-container .dtr-primary-result__radical { font-size: 1.5em; transform: translateY(0.05em); }\r\n        \r\n        \/* Breakdown Accordion *\/\r\n        .dtr-container .dtr__breakdown { border-top: 1px solid var(--dtr-border); margin-top: 30px; padding-top: 20px; }\r\n        .dtr-container .dtr__breakdown-toggle { display: flex; justify-content: space-between; align-items: center; background: none; border: none; width: 100%; padding: 10px 0; cursor: pointer; text-align: left; font-family: inherit; }\r\n        .dtr-container .dtr__breakdown-label { font-size: 1rem; font-weight: 700; color: var(--dtr-text-primary); }\r\n        .dtr-container .dtr__breakdown-chevron { color: var(--dtr-accent); transition: transform 0.3s ease; }\r\n        .dtr-container .dtr__breakdown--open .dtr__breakdown-chevron { transform: rotate(180deg); }\r\n        .dtr-container .dtr__breakdown-content { max-height: 0; overflow: hidden; transition: max-height 0.4s ease-out; font-family: var(--dtr-font-serif); color: var(--dtr-text-secondary); font-size: 1.1rem; line-height: 1.8; }\r\n        .dtr-container .dtr__breakdown-content p { padding-top: 20px; margin-bottom: 1em; }\r\n        .dtr-container .dtr__breakdown-content strong { color: var(--dtr-text-primary); }\r\n        \r\n        \/* --- RESPONSIVENESS --- *\/\r\n        @media (max-width: 1024px) {\r\n            .dtr-container .dtr-card__grid { grid-template-columns: 300px 1fr; gap: 40px; } \/* Slightly smaller fixed width *\/\r\n            .dtr-container .dtr-primary-result { font-size: 5rem; }\r\n            .dtr-container .dtr-primary-result--shrunk { font-size: 3rem; }\r\n            .dtr-container .dtr__input { font-size: 2rem; }\r\n        }\r\n        @media (max-width: 768px) {\r\n            \/* On tablet, abandon fixed width and stack *\/\r\n            .dtr-container .dtr-card__grid { grid-template-columns: 1fr; }\r\n            .dtr-container .dtr-card__results-dashboard { border-top: 1px solid var(--dtr-border); margin-top: 40px; padding-top: 40px; }\r\n            .dtr-container .dtr-hero-content__title { font-size: 3rem; }\r\n        }\r\n        @media (max-width: 576px) {\r\n            .dtr-container .dtr-hero-wrapper { padding: 0 20px; }\r\n            .dtr-container { padding: 100px 0; }\r\n            .dtr-container .dtr-card { padding: 40px 30px; }\r\n            .dtr-container .dtr-hero-content__title { font-size: 2.5rem; }\r\n            .dtr-container .dtr-primary-result { font-size: 4rem; min-height: 90px;}\r\n            .dtr-container .dtr-primary-result--shrunk { font-size: 2.5rem; }\r\n        }\r\n        @media (max-width: 480px) {\r\n            .dtr-container .dtr-hero-content__title { font-size: 2.2rem; }\r\n            .dtr-container .dtr-primary-result { font-size: 31px; }\r\n            .dtr-container .dtr-primary-result--shrunk { font-size: 2.2rem; }\r\n        }\r\n        @media (max-width: 375px) {\r\n            .dtr-container .dtr-hero-wrapper { padding: 0 15px; }\r\n            .dtr-container .dtr-card { padding: 30px 25px; }\r\n        }\r\n    <\/style>\r\n    \r\n    <div class=\"dtr-hero-wrapper\">\r\n        <div id=\"dtr-hero-content\" class=\"dtr-hero-content\">\r\n            <h1 class=\"dtr-hero-content__title\">Decimal to Radical <span class=\"dtr-hero-content__highlight\">Calculator.<\/span><\/h1>\r\n            <p class=\"dtr-hero-content__subtitle\">Translate complex decimals into their pure, simplified radical form. A precision tool for students, engineers, and mathematicians.<\/p>\r\n        <\/div>\r\n        \r\n        <div id=\"dtr-card\" class=\"dtr-card\">\r\n            <div class=\"dtr-card__grid\">\r\n                <div class=\"dtr-card__input-deck\">\r\n                     <label for=\"dtr-input\" class=\"dtr-section__label\">Enter a decimal<\/label>\r\n                     <input type=\"text\" id=\"dtr-input\" class=\"dtr__input\" inputmode=\"decimal\" placeholder=\"2.828\">\r\n                <\/div>\r\n                <div class=\"dtr-card__results-dashboard\">\r\n                    <div>\r\n                        <label class=\"dtr-section__label\">Simplified Radical Form<\/label>\r\n                        <div id=\"dtr-primary-result\" class=\"dtr-primary-result\">\r\n                            <span id=\"dtr-result-coeff\" class=\"dtr-primary-result__coeff\"><\/span>\r\n                            <span class=\"dtr-primary-result__radical\">\u221a<span id=\"dtr-result-radicand\" class=\"dtr-primary-result__radicand\">0<\/span><\/span>\r\n                        <\/div>\r\n                    <\/div>\r\n                    <div id=\"dtr-breakdown\" class=\"dtr__breakdown\">\r\n                        <button id=\"dtr-breakdown-toggle\" class=\"dtr__breakdown-toggle\">\r\n                            <span class=\"dtr__breakdown-label\">Show Simplification<\/span>\r\n                            <svg class=\"dtr__breakdown-chevron\" width=\"24\" height=\"24\" viewBox=\"0 0 24 24\"><path fill=\"currentColor\" d=\"M7.41 8.58L12 13.17l4.59-4.59L18 10l-6 6l-6-6l1.41-1.42Z\"\/><\/svg>\r\n                        <\/button>\r\n                        <div id=\"dtr-breakdown-content\" class=\"dtr__breakdown-content\"><\/div>\r\n                    <\/div>\r\n                <\/div>\r\n            <\/div>\r\n        <\/div>\r\n    <\/div>\r\n    \r\n    <script>\r\n    (() => {\r\n        document.addEventListener('DOMContentLoaded', () => {\r\n            const elements = {\r\n                heroContent: document.getElementById('dtr-hero-content'),\r\n                card: document.getElementById('dtr-card'),\r\n                input: document.getElementById('dtr-input'),\r\n                primaryResult: document.getElementById('dtr-primary-result'),\r\n                coeff: document.getElementById('dtr-result-coeff'),\r\n                radicand: document.getElementById('dtr-result-radicand'),\r\n                breakdown: document.getElementById('dtr-breakdown'),\r\n                breakdownToggle: document.getElementById('dtr-breakdown-toggle'),\r\n                breakdownContent: document.getElementById('dtr-breakdown-content'),\r\n            };\r\n\r\n            function gcd(a, b) { return b === 0 ? a : gcd(b, a % b); }\r\n\r\n            function simplifyRadical(n) {\r\n                if (n < 0) return { coeff: NaN, radicand: n, factors: [] };\r\n                if (n === 0) return { coeff: 0, radicand: 1, factors: [] };\r\n                let coeff = 1, radicand = n;\r\n                for (let i = 2; i * i <= radicand; i++) {\r\n                    while (radicand % (i * i) === 0) {\r\n                        coeff *= i;\r\n                        radicand \/= (i * i);\r\n                    }\r\n                }\r\n                let factors = getPrimeFactors(n);\r\n                return { coeff, radicand, factors };\r\n            }\r\n\r\n            function getPrimeFactors(n) {\r\n                const factors = []; let divisor = 2;\r\n                while (n >= 2) {\r\n                    if (n % divisor === 0) { factors.push(divisor); n \/= divisor; } else { divisor++; }\r\n                }\r\n                return factors;\r\n            }\r\n\r\n            function updateRadical() {\r\n                const value = parseFloat(elements.input.value);\r\n                if (isNaN(value)) { renderResult(1, 0, null); return; }\r\n\r\n                let len = (elements.input.value.toString().split('.')[1] || '').length;\r\n                let denominator = 10 ** Math.min(len, 9); \/\/ Limit precision to prevent overflow\r\n                let numerator = Math.round(value * denominator);\r\n                \r\n                let common = gcd(numerator, denominator);\r\n                numerator \/= common;\r\n                denominator \/= common;\r\n\r\n                const simplifiedNum = simplifyRadical(numerator);\r\n                const simplifiedDen = simplifyRadical(denominator);\r\n\r\n                let finalCoeffNum = simplifiedNum.coeff;\r\n                let finalRadicandNum = simplifiedNum.radicand;\r\n                let finalCoeffDen = simplifiedDen.coeff;\r\n                let finalRadicandDen = simplifiedDen.radicand;\r\n\r\n                let finalRadicand = finalRadicandNum * finalRadicandDen;\r\n                let finalCoeff = finalCoeffNum * finalRadicandDen;\r\n                let finalDenom = finalCoeffDen * finalRadicand;\r\n\r\n                let simplifiedFinalRadical = simplifyRadical(finalRadicand);\r\n                finalCoeff *= simplifiedFinalRadical.coeff;\r\n                finalRadicand = simplifiedFinalRadical.radicand;\r\n\r\n                let commonFinal = gcd(finalCoeff, finalDenom);\r\n                finalCoeff \/= commonFinal;\r\n                finalDenom \/= commonFinal;\r\n\r\n                const displayCoeff = finalDenom === 1 ? finalCoeff : `${finalCoeff}\/${finalDenom}`;\r\n                renderResult(displayCoeff, finalRadicand, { numerator, denominator, simplifiedNum, simplifiedDen });\r\n            }\r\n            \r\n            \/\/ --- NEW: DYNAMIC FONT SIZING ---\r\n            function adjustResultFontSize() {\r\n                const container = elements.primaryResult;\r\n                const coeffEl = elements.coeff;\r\n                const radicandEl = elements.radicand;\r\n\r\n                \/\/ Reset first to allow it to grow back\r\n                container.classList.remove('dtr-primary-result--shrunk');\r\n\r\n                \/\/ Use requestAnimationFrame to check size after browser has re-rendered\r\n                requestAnimationFrame(() => {\r\n                    const coeffLength = coeffEl.textContent.length;\r\n                    const radicandLength = radicandEl.textContent.length;\r\n                    \r\n                    \/\/ Check if either part is too long\r\n                    if (coeffLength > 5 || radicandLength > 5) {\r\n                        container.classList.add('dtr-primary-result--shrunk');\r\n                    }\r\n                });\r\n            }\r\n\r\n            function renderResult(coeff, radicand, breakdownData) {\r\n                elements.coeff.textContent = (coeff === 1 && radicand !== 1) ? '' : coeff;\r\n                elements.radicand.textContent = radicand;\r\n                elements.radicand.parentElement.style.display = (radicand === 1 && coeff !== 0) ? 'none' : 'inline';\r\n\r\n                if (breakdownData) {\r\n                    elements.breakdownContent.innerHTML = generateBreakdownHTML(breakdownData);\r\n                } else {\r\n                    elements.breakdownContent.innerHTML = '<p>Enter a valid decimal to see the simplification.<\/p>';\r\n                }\r\n                \r\n                \/\/ Call the new font adjustment function AFTER rendering\r\n                adjustResultFontSize();\r\n            }\r\n\r\n            function generateBreakdownHTML({ numerator, denominator, simplifiedNum, simplifiedDen }) {\r\n                 let html = `<p><strong>1. Convert to Fraction:<\/strong><br> ${elements.input.value} \u2248 ${numerator} \/ ${denominator}<\/p>`;\r\n                html += `<p><strong>2. Simplify Numerator:<\/strong><br> \u221a${numerator} \u2248 \u221a(${simplifiedNum.factors.join(' \u00d7 ')}) = <strong>${simplifiedNum.coeff}\u221a${simplifiedNum.radicand}<\/strong><\/p>`;\r\n                html += `<p><strong>3. Simplify Denominator:<\/strong><br> \u221a${denominator} \u2248 \u221a(${simplifiedDen.factors.join(' \u00d7 ')}) = <strong>${simplifiedDen.coeff}\u221a${simplifiedDen.radicand}<\/strong><\/p>`;\r\n                html += `<p><strong>4. Combine & Rationalize:<\/strong><br> The parts are combined and simplified to produce the final radical form.<\/p>`;\r\n                return html;\r\n            }\r\n\r\n            elements.input.addEventListener('input', updateRadical);\r\n            elements.breakdownToggle.addEventListener('click', () => {\r\n                const content = elements.breakdownContent;\r\n                elements.breakdown.classList.toggle('dtr__breakdown--open');\r\n                if (content.style.maxHeight) { content.style.maxHeight = null; } \r\n                else { content.style.maxHeight = content.scrollHeight + \"px\"; }\r\n            });\r\n\r\n            setTimeout(() => {\r\n                elements.heroContent.classList.add('dtr-hero-content--loaded');\r\n                elements.card.classList.add('dtr-card--loaded');\r\n            }, 50);\r\n\r\n            updateRadical();\r\n        });\r\n    })();\r\n    <\/script>\r\n<\/div>\r\n<!-- END: Decimal to Radical Calculator Hero Block -->\r\n<!-- Start of the Supportive Content Section -->\r\n<div class=\"dtr-container dtr-support-content\">\r\n    <style>\r\n        \/* FONT IMPORT *\/\r\n        @import url('https:\/\/fonts.googleapis.com\/css2?family=Satoshi:wght@400;700&display=swap');\r\n        @import url('https:\/\/fonts.googleapis.com\/css2?family=Source+Serif+4:opsz,wght@8..60,600&display=swap');\r\n\r\n        \/* CSS VARIABLES *\/\r\n        .dtr-container {\r\n            --dtr-bg-start: #f1f1f1;\r\n            --dtr-bg-end: #ffffff;\r\n            --dtr-panel: #FFFFFF;\r\n            --dtr-accent: #192A51;\r\n            --dtr-text-primary: #192A51;\r\n            --dtr-text-secondary: #79829B;\r\n            --dtr-input-bg: #F4F6FB;\r\n            --dtr-border: #E1E6F0;\r\n            --dtr-shadow: rgba(25, 42, 81, 0.1);\r\n            --dtr-font-primary: 'Satoshi', 'Inter', sans-serif;\r\n            --dtr-font-serif: 'Source Serif 4', serif;\r\n            --dtr-radius: 20px;\r\n        }\r\n\r\n        \/* --- BULLETPROOF BASE & HERO LAYOUT --- *\/\r\n        .dtr-container { font-family: var(--dtr-font-primary); background: linear-gradient(135deg, var(--dtr-bg-start) 0%, var(--dtr-bg-end) 100%); padding: 60px 0; width: 100%; position: relative; box-sizing: border-box; }\r\n        .dtr-container *, .dtr-container *::before, .dtr-container *::after { box-sizing: inherit; }\r\n        .dtr-container h2, .dtr-container h3, .dtr-container p, .dtr-container ul, .dtr-container ol { margin: 0; padding: 0; font: inherit; }\r\n\r\n        \/* --- SUPPORTIVE CONTENT STYLES --- *\/\r\n        .dtr-support-content { padding-top: 0; }\r\n        .dtr-container .dtr-support-wrapper { max-width: 1160px; margin: 0 auto; padding: 0 40px; }\r\n        .dtr-info-section {\r\n            padding: 4.5rem 0;\r\n            border-bottom: 1px solid var(--dtr-border);\r\n        }\r\n        .dtr-support-content .dtr-support-wrapper > .dtr-info-section:last-child {\r\n            border-bottom: none;\r\n        }\r\n\r\n        .dtr-container .dtr-section-heading {\r\n            font-size: 2.5rem;\r\n            font-weight: 700;\r\n            color: var(--dtr-text-primary);\r\n            text-align: center;\r\n            margin-bottom: 1rem;\r\n        }\r\n        .dtr-container .dtr-section-heading span { color: var(--dtr-accent); }\r\n\r\n        .dtr-container .dtr-section-subheading {\r\n            font-size: 1.1rem;\r\n            color: var(--dtr-text-secondary);\r\n            text-align: center;\r\n            max-width: 700px;\r\n            margin: 0 auto 3.5rem auto;\r\n            line-height: 1.6;\r\n        }\r\n\r\n        \/* Card Grid Layout *\/\r\n        .dtr-container .dtr-card-grid {\r\n            display: grid;\r\n            grid-template-columns: repeat(3, 1fr);\r\n            gap: 1.5rem;\r\n        }\r\n        \r\n        .dtr-container .dtr-info-card {\r\n            background: var(--dtr-panel);\r\n            border-radius: var(--dtr-radius);\r\n            padding: 2rem;\r\n            text-align: center;\r\n            box-shadow: 0 15px 40px -10px var(--dtr-shadow);\r\n            border: 1px solid #fff;\r\n            transition: transform 0.3s ease, box-shadow 0.3s ease;\r\n        }\r\n        .dtr-container .dtr-info-card:hover {\r\n            transform: translateY(-8px);\r\n            box-shadow: 0 20px 50px -15px var(--dtr-shadow);\r\n        }\r\n        \r\n        .dtr-container .dtr-card-icon {\r\n            display: flex;\r\n            align-items: center;\r\n            justify-content: center;\r\n            width: 60px;\r\n            height: 60px;\r\n            margin: 0 auto 1.5rem auto;\r\n            border-radius: 16px;\r\n            background-color: var(--dtr-input-bg);\r\n            color: var(--dtr-accent);\r\n            border: 1px solid var(--dtr-border);\r\n        }\r\n        .dtr-container .dtr-card-icon svg { width: 28px; height: 28px; }\r\n\r\n        .dtr-container .dtr-info-card h3 {\r\n            font-size: 1.125rem;\r\n            font-weight: 700;\r\n            margin-top: 0;\r\n            margin-bottom: 0.75rem;\r\n            color: var(--dtr-text-primary);\r\n        }\r\n\r\n        .dtr-container .dtr-info-card p, .dtr-container .dtr-info-card ol {\r\n            font-size: 0.95rem;\r\n            color: var(--dtr-text-secondary);\r\n            line-height: 1.6;\r\n            margin: 0;\r\n            text-align: left;\r\n        }\r\n        .dtr-container .dtr-info-card ol { list-style-position: inside; }\r\n        \r\n        \/* Two-Column Feature Section *\/\r\n        .dtr-container .dtr-feature-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 3rem; align-items: center; }\r\n        .dtr-container .dtr-feature-grid .dtr-section-heading, .dtr-container .dtr-feature-grid .dtr-section-subheading { text-align: left; margin-left: 0; }\r\n        .dtr-container .dtr-feature-list { list-style: none; padding: 0; margin: 0; display: flex; flex-direction: column; gap: 1.5rem; }\r\n        .dtr-container .dtr-feature-item { display: flex; align-items: flex-start; gap: 1rem; font-size: 1rem; }\r\n        .dtr-container .dtr-feature-item svg { flex-shrink: 0; width: 24px; height: 24px; color: var(--dtr-accent); margin-top: 2px; }\r\n        .dtr-container .dtr-feature-item strong { color: var(--dtr-text-primary); font-weight: 700; }\r\n        \r\n        \/* FAQ Section *\/\r\n        .dtr-container .dtr-faq-container { max-width: 800px; margin: 0 auto; display: flex; flex-direction: column; gap: 1rem; }\r\n        .dtr-container .dtr-faq-item { background: var(--dtr-panel); border: 1px solid #fff; box-shadow: 0 10px 30px -10px var(--dtr-shadow); border-radius: var(--dtr-radius); }\r\n        .dtr-container .dtr-faq-question {\r\n            padding: 1.25rem 1.5rem; font-size: 1.05rem; font-weight: 700; cursor: pointer; display: flex; justify-content: space-between; align-items: center; color: var(--dtr-text-primary); list-style: none;\r\n        }\r\n        .dtr-container .dtr-faq-question::-webkit-details-marker { display: none; }\r\n        .dtr-container .dtr-faq-icon { transition: transform 0.3s ease; width: 20px; height: 20px; color: var(--dtr-text-secondary); }\r\n        .dtr-container .dtr-faq-item[open] .dtr-faq-icon { transform: rotate(180deg); }\r\n        .dtr-container .dtr-faq-answer { padding: 0 1.5rem 1.5rem 1.5rem; color: var(--dtr-text-secondary); line-height: 1.7; }\r\n        .dtr-container .dtr-faq-answer strong { color: var(--dtr-text-primary); }\r\n        .dtr-container .dtr-faq-answer code {\r\n             font-family: var(--dtr-font-serif); font-weight: 600;\r\n             background-color: var(--dtr-input-bg); padding: 0.1rem 0.4rem; border-radius: 4px;\r\n        }\r\n        \r\n        \/* Responsive Design *\/\r\n        @media (max-width: 768px) {\r\n            .dtr-container .dtr-section-heading { font-size: 2.25rem; }\r\n            .dtr-container .dtr-card-grid, .dtr-container .dtr-feature-grid { grid-template-columns: 1fr; }\r\n            .dtr-container .dtr-feature-grid .dtr-section-heading, .dtr-container .dtr-feature-grid .dtr-section-subheading { text-align: center; margin-left: auto; margin-right: auto; }\r\n        }\r\n        @media (max-width: 576px) {\r\n            .dtr-container .dtr-support-wrapper { padding: 0 20px; }\r\n            .dtr-container .dtr-section-heading { font-size: 2rem; }\r\n            .dtr-container .dtr-section-subheading { font-size: 1rem; }\r\n            .dtr-container .dtr-info-card, .dtr-container .dtr-faq-question, .dtr-container .dtr-faq-answer { padding: 1.5rem; }\r\n        }\r\n    <\/style>\r\n\r\n    <div class=\"dtr-support-wrapper\">\r\n\r\n        <!-- 1. What is a Radical? -->\r\n        <section class=\"dtr-info-section\">\r\n            <h2 class=\"dtr-section-heading\">What is a <span>Radical<\/span>?<\/h2>\r\n            <p class=\"dtr-section-subheading\">In mathematics, a radical expression is any expression containing a radical symbol (\u221a). It represents the root of a number. This calculator focuses on converting decimals to their most elegant and precise form: the simplified radical.<\/p>\r\n            <div class=\"dtr-card-grid\">\r\n                <div class=\"dtr-info-card\">\r\n                    <h3>Precision over Approximation<\/h3>\r\n                    <p>Decimals like 1.414... are approximations of irrational numbers. The radical form, \u221a2, is the exact and pure representation of that value, crucial in higher mathematics and engineering.<\/p>\r\n                <\/div>\r\n                <div class=\"dtr-info-card\">\r\n                    <h3>Simplified Form<\/h3>\r\n                    <p>A radical is \"simplified\" when the number under the radical sign (the radicand) has no perfect square factors. For example, \u221a12 is not simplified because it contains the perfect square factor 4. It simplifies to 2\u221a3.<\/p>\r\n                <\/div>\r\n                <div class=\"dtr-info-card\">\r\n                    <h3>Key Components<\/h3>\r\n                    <p>A radical has three main parts: the <strong>radicand<\/strong> (the number inside), the <strong>coefficient<\/strong> (the number outside), and the <strong>radical symbol<\/strong> (\u221a).<\/p>\r\n                <\/div>\r\n            <\/div>\r\n        <\/section>\r\n\r\n        <!-- 2. The Conversion Process -->\r\n        <section class=\"dtr-info-section\">\r\n            <h2 class=\"dtr-section-heading\">The Conversion <span>Process<\/span><\/h2>\r\n            <p class=\"dtr-section-subheading\">Our calculator uses a multi-step mathematical process to convert a decimal into its simplified radical equivalent.<\/p>\r\n            <div class=\"dtr-card-grid\">\r\n                 <div class=\"dtr-info-card\">\r\n                    <h3>1. Convert to a Fraction<\/h3>\r\n                    <p>The first step is to convert the input decimal into a fraction. For example, <code>1.5<\/code> becomes <code>15\/10<\/code>, which simplifies to <code>3\/2<\/code>.<\/p>\r\n                <\/div>\r\n                <div class=\"dtr-info-card\">\r\n                    <h3>2. Separate Numerator & Denominator<\/h3>\r\n                    <p>The radical of a fraction is equal to the radical of the numerator divided by the radical of the denominator: \u221a(3\/2) = \u221a3 \/ \u221a2.<\/p>\r\n                <\/div>\r\n                <div class=\"dtr-info-card\">\r\n                    <h3>3. Simplify and Rationalize<\/h3>\r\n                    <p>Each radical (numerator and denominator) is simplified by pulling out perfect squares. Finally, the denominator is \"rationalized\" to remove any radicals from the bottom of the fraction.<\/p>\r\n                <\/div>\r\n            <\/div>\r\n        <\/section>\r\n\r\n        <!-- 3. Features of This Calculator -->\r\n        <section class=\"dtr-info-section\">\r\n            <div class=\"dtr-feature-grid\">\r\n                <div>\r\n                    <h2 class=\"dtr-section-heading\" style=\"text-align:left;\">Features of the <span>Engine<\/span><\/h2>\r\n                    <p class=\"dtr-section-subheading\" style=\"text-align:left;\">This tool is engineered for precision, clarity, and a seamless user experience, making complex conversions simple.<\/p>\r\n                <\/div>\r\n                <div>\r\n                    <ul class=\"dtr-feature-list\">\r\n                        <li class=\"dtr-feature-item\">\r\n                            <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" fill=\"none\" viewBox=\"0 0 24 24\" stroke-width=\"1.5\" stroke=\"currentColor\"><path stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M3.75 3v11.25A2.25 2.25 0 006 16.5h2.25M3.75 3h-1.5m1.5 0h16.5m0 0h1.5m-1.5 0v11.25A2.25 2.25 0 0118 16.5h-2.25m-7.5 0h7.5m-7.5 0l-1 1.5m1-1.5l1 1.5m0 0l.5 1.5m.5-1.5h.5m2.25-3l-3-3m0 0l-3 3m3-3v6m0 0l3 3m-3-3l-3 3\" \/><\/svg>\r\n                            <span><strong>Live Conversion:<\/strong> The radical form updates instantly as you type, providing immediate feedback without needing to click a button.<\/span>\r\n                        <\/li>\r\n                        <li class=\"dtr-feature-item\">\r\n                           <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" fill=\"none\" viewBox=\"0 0 24 24\" stroke-width=\"1.5\" stroke=\"currentColor\"><path stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M10.5 6a7.5 7.5 0 100 15 7.5 7.5 0 000-15zM21 21l-5.2-5.2\" \/><\/svg>\r\n                            <span><strong>Detailed Breakdown:<\/strong> Click \"Show Simplification\" to see a step-by-step explanation of how the calculator arrived at the final answer, perfect for students.<\/span>\r\n                        <\/li>\r\n                         <li class=\"dtr-feature-item\">\r\n                           <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" fill=\"none\" viewBox=\"0 0 24 24\" stroke-width=\"1.5\" stroke=\"currentColor\"><path stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9.75 3.104v5.714a2.25 2.25 0 01-.659 1.591L5 14.5M9.75 3.104c.252 0 .487.021.727.062a4.501 4.501 0 014.23 4.23c.041.24.062.475.062.727v5.714a2.25 2.25 0 002.25 2.25H15M9.75 3.104C11.625 2.164 14.125 2 16.5 2c3.314 0 6 2.686 6 6v6.5a2.5 2.5 0 01-2.5 2.5H15\" \/><\/svg>\r\n                            <span><strong>Auto-Scaling Output:<\/strong> The result display intelligently shrinks its font size to accommodate very large numbers, ensuring your answer is never cut off.<\/span>\r\n                        <\/li>\r\n                    <\/ul>\r\n                <\/div>\r\n            <\/div>\r\n        <\/section>\r\n\r\n        <!-- 4. Frequently Asked Questions -->\r\n        <section class=\"dtr-info-section\">\r\n            <h2 class=\"dtr-section-heading\">Frequently Asked <span>Questions<\/span><\/h2>\r\n            <p class=\"dtr-section-subheading\">Get quick answers to common questions about converting decimals to radicals.<\/p>\r\n            <div class=\"dtr-faq-container\">\r\n                <details class=\"dtr-faq-item\">\r\n                    <summary class=\"dtr-faq-question\">\r\n                        <span>Why does the calculator sometimes show a fraction in front of the radical?<\/span>\r\n                        <svg class=\"dtr-faq-icon\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" fill=\"none\" viewBox=\"0 0 24 24\" stroke-width=\"2\" stroke=\"currentColor\"><path stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M19 9l-7 7-7-7\" \/><\/svg>\r\n                    <\/summary>\r\n                    <div class=\"dtr-faq-answer\">\r\n                        <p>This happens when the process of \"rationalizing the denominator\" results in a final fraction. For example, converting <code>0.5<\/code> first becomes <code>\u221a(1\/2)<\/code>, which is <code>1\/\u221a2<\/code>. To remove the radical from the denominator, we multiply the top and bottom by <code>\u221a2<\/code>, resulting in the final simplified answer of <strong>(1\/2)\u221a2<\/strong>.<\/p>\r\n                    <\/div>\r\n                <\/details>\r\n                <details class=\"dtr-faq-item\">\r\n                    <summary class=\"dtr-faq-question\">\r\n                        <span>Can I convert a repeating decimal?<\/span>\r\n                        <svg class=\"dtr-faq-icon\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" fill=\"none\" viewBox=\"0 0 24 24\" stroke-width=\"2\" stroke=\"currentColor\"><path stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M19 9l-7 7-7-7\" \/><\/svg>\r\n                    <\/summary>\r\n                    <div class=\"dtr-faq-answer\">\r\n                        <p>Currently, the calculator handles terminating decimals. Converting repeating decimals (like 0.333...) to a fraction requires a different algebraic method that is not yet implemented. For now, you can approximate a repeating decimal by entering a long version of it (e.g., <code>0.33333333<\/code>).<\/p>\r\n                    <\/div>\r\n                <\/details>\r\n                 <details class=\"dtr-faq-item\">\r\n                    <summary class=\"dtr-faq-question\">\r\n                        <span>What is the largest number I can convert?<\/span>\r\n                        <svg class=\"dtr-faq-icon\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" fill=\"none\" viewBox=\"0 0 24 24\" stroke-width=\"2\" stroke=\"currentColor\"><path stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M19 9l-7 7-7-7\" \/><\/svg>\r\n                    <\/summary>\r\n                    <div class=\"dtr-faq-answer\">\r\n                        <p>The calculator is limited by JavaScript's maximum precision for floating-point numbers. For the most accurate results, it's best to use decimals with nine or fewer decimal places. Very long decimals may result in a less precise fractional conversion, which can affect the final radical form.<\/p>\r\n                    <\/div>\r\n                <\/details>\r\n            <\/div>\r\n        <\/section>\r\n\r\n    <\/div>\r\n<\/div>\r\n<!-- End of the Supportive Content Section --><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-homepage.php","meta":{"footnotes":""},"class_list":["post-5451","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Calculadora de Decimal para Radical \u2013 Converta N\u00fameros Facilmente<\/title>\n<meta name=\"description\" content=\"Converta decimais em radicais ou ra\u00edzes instantaneamente. Ferramenta online gratuita para \u00e1lgebra, equa\u00e7\u00f5es e pr\u00e1tica matem\u00e1tica precisa.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sigfigcalculator.io\/pt\/decimal-to-radical-calculator\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Decimal to Radical Calculator \u2013 Convert Numbers Easily\" \/>\n<meta property=\"og:description\" content=\"Convert decimals into radical or root form instantly. Free online tool for algebra, equations, and accurate math practice.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/\" \/>\n<meta property=\"og:site_name\" content=\"SigFig Calculator\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/decimal-to-radical-calculator\\\/\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/decimal-to-radical-calculator\\\/\",\"name\":\"Decimal to Radical Calculator \u2013 Convert Numbers Easily\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#website\"},\"datePublished\":\"2025-10-01T08:35:40+00:00\",\"description\":\"Convert decimals into radical or root form instantly. Free online tool for algebra, equations, and accurate math practice.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/decimal-to-radical-calculator\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/sigfigcalculator.io\\\/decimal-to-radical-calculator\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/decimal-to-radical-calculator\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/sigfigcalculator.io\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Decimal to Radical Calculator \u2013 Convert Numbers Easily\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/sigfigcalculator.io\\\/#website\",\"url\":\"https:\\\/\\\/sigfigcalculator.io\\\/\",\"name\":\"SigFig Calculator\",\"description\":\"Your tool for perfect scientific accuracy\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/sigfigcalculator.io\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Calculadora de Decimal para Radical \u2013 Converta N\u00fameros Facilmente","description":"Converta decimais em radicais ou ra\u00edzes instantaneamente. Ferramenta online gratuita para \u00e1lgebra, equa\u00e7\u00f5es e pr\u00e1tica matem\u00e1tica precisa.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sigfigcalculator.io\/pt\/decimal-to-radical-calculator\/","og_locale":"en_US","og_type":"article","og_title":"Decimal to Radical Calculator \u2013 Convert Numbers Easily","og_description":"Convert decimals into radical or root form instantly. Free online tool for algebra, equations, and accurate math practice.","og_url":"https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/","og_site_name":"SigFig Calculator","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/","url":"https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/","name":"Decimal to Radical Calculator \u2013 Convert Numbers Easily","isPartOf":{"@id":"https:\/\/sigfigcalculator.io\/#website"},"datePublished":"2025-10-01T08:35:40+00:00","description":"Convert decimals into radical or root form instantly. Free online tool for algebra, equations, and accurate math practice.","breadcrumb":{"@id":"https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sigfigcalculator.io\/decimal-to-radical-calculator\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sigfigcalculator.io\/"},{"@type":"ListItem","position":2,"name":"Decimal to Radical Calculator \u2013 Convert Numbers Easily"}]},{"@type":"WebSite","@id":"https:\/\/sigfigcalculator.io\/#website","url":"https:\/\/sigfigcalculator.io\/","name":"SigFig Calculator","description":"Your tool for perfect scientific accuracy","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sigfigcalculator.io\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/pages\/5451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/comments?post=5451"}],"version-history":[{"count":4,"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/pages\/5451\/revisions"}],"predecessor-version":[{"id":5455,"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/pages\/5451\/revisions\/5455"}],"wp:attachment":[{"href":"https:\/\/sigfigcalculator.io\/pt\/wp-json\/wp\/v2\/media?parent=5451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}