Radical Expression Simplifier Calculator
Simplify Radical Expressions works out Root and Rounded root from Number, Coefficient in front of the radical and Decimal places. The default figures on this page give root of 8.485281; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- Prime-factorise 72 and pull out every complete group of 2: 72 = 6^2 x 2.
- So the exact form is 6 sqrt(2).
- Decimal value: 8.48528137424 = 8.48528137424.
- An even root has two real branches: +8.48528137424 and -8.48528137424.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Simplify Radical Expressions calculates
Finds the square root, cube root or any nth root of a number, simplifies the exact radical form, reports the negative branch, and names the imaginary root when an even root of a negative number is asked for.
How to use this Simplify Radical Expressions
Enter Number, Coefficient in front of the radical, Decimal places and Principal root only. Root updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Root, Rounded root and Exact (simplified radical).
The method follows NIST Digital Library of Mathematical Functions, 4.2(i) Powers and Roots and Fundamental theorem of arithmetic (unique prime factorisation), Hardy & Wright, An Introduction to the Theory of Numbers, Theorem 2.
What you can compare
Change one input at a time to see how it affects Root, Rounded root and Exact (simplified radical). The inputs you can vary are Number, Coefficient in front of the radical, Decimal places and Principal root only.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
How to simplify a radical on a calculator?
Finds the square root, cube root or any nth root of a number, simplifies the exact radical form, reports the negative branch, and names the imaginary root when an even root of a negative number is asked for. Open “How this is worked out” beside the result to see each step for your own figures.
Can my TI-84 simplify radicals?
Finds the square root, cube root or any nth root of a number, simplifies the exact radical form, reports the negative branch, and names the imaginary root when an even root of a negative number is asked for. On the figures this page opens with — number 144 — the root is 8.485281. Put your own figures in their place and the working updates beside the result.
Is there a formula for simplifying radicals?
It needs Number, Coefficient in front of the radical, Decimal places and Principal root only. Nothing else is required, and the figures stay in your browser.
How can I simplify radical equations?
The result gives Root, Rounded root, Exact (simplified radical), Factor outside the radical, Radicand left inside and Perfect power?, each labelled with its unit so the figure can be read on its own.
What information do I need for the Simplify Radical Expressions?
You need Number, Coefficient in front of the radical, Decimal places and Principal root only. The page opens with default figures that give root of 8.485281, so you can see the scale before entering your own.
What does this Simplify Radical Expressions show?
It shows Root, Rounded root, Exact (simplified radical), Factor outside the radical, Radicand left inside, Perfect power?, Negative branch and Imaginary root, with the working and any warnings for your entries.