Find Square Root Calculator
Square Root and Nth Root Calculator works out Root and Rounded root from Number, Root index and Coefficient in front of the radical. The default figures on this page give root of 12; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- 144 is a perfect square: 12^2 = 144.
- Decimal value: 12 = 12.
- An even root has two real branches: +12 and -12.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Square Root and Nth Root Calculator 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 Square Root and Nth Root Calculator
Enter Number, Root index, Coefficient in front of the radical and Decimal places. Root updates as you type, and “Use a worked example” loads checked figures you can adjust. 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.
Square root of 144 example
With Number: 144, Root index: 2, the calculator returns Root: 12, Exact (simplified radical): 12, Perfect power?: true. This example is checked against an independent source in the test suite.
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, Root index, 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.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do I do the square root 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.
How to square root on a TI-84 calculator?
It needs Number, Root index, Coefficient in front of the radical, Decimal places and Principal root only. Nothing else is required, and the figures stay in your browser.
What information do I need for the Square Root and Nth Root Calculator?
You need Number, Root index, Coefficient in front of the radical, Decimal places and Principal root only. The page opens with default figures that give root of 12, so you can see the scale before entering your own.
What does this Square Root and Nth Root Calculator 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.
Can I check how the Square Root and Nth Root Calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.