Square root
root_2(144)12 because 12^2 = 144
Root Calculator
Use this free root calculator to find square roots, cube roots, and nth roots with real-number guardrails, exponent form, power checks, decimal examples, and steps.
Square rootsCube rootsNth rootsExponent form
root_2(144)12
- Exponent form
- 1/2
- Power check
- 144
- Root type
- square root
Steps
- Start with the square root of 144.
- Rewrite the root as a rational exponent: 144^(1/2).
- That exponent is 0.5.
- The answer is 12, because 12^2 returns 144.
Recent answers
Recent root answers will appear here.
Input tips
Use index 2 for square roots and index 3 for cube roots.
Negative radicands need an odd whole-number root index for real-number answers.
How to use the Root Calculator
- Enter the radicand, which is the value inside the root.
- Enter a whole-number root index, such as 2 for square root or 3 for cube root.
- Press Calculate root to see the answer, exponent form, power check, and steps.
- Use examples, recent answers, or copy the answer while checking root problems.
What people use it for
Find square roots and cube roots for math, science, and study problems.
Calculate nth roots such as fourth roots, fifth roots, and higher whole-number roots.
Convert root notation into rational exponent form.
Check whether a negative radicand has a real-number root.
Check decimal roots such as the cube root of 0.008.
Raise the answer back to the root index to verify the power check.
Quick examples
Cube root
root_3(-125)-5 because (-5)^3 = -125
Fourth root
root_4(81)3 because 3^4 = 81
Fifth root
root_5(32)2 because 2^5 = 32
Decimal cube root
root_3(0.008)0.2 because 0.2^3 = 0.008
Even root of a negative
root_2(-16)No real-number result
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Root CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
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Frequently asked questions
Quick answers about square roots, cube roots, nth roots, negative radicands, exponent form, and privacy.
What is an nth root?
An nth root asks what number raised to the nth power gives the radicand. For example, the cube root of 125 is 5 because 5^3 = 125.
What is the difference between square root and cube root?
A square root uses index 2, so the answer squared returns the radicand. A cube root uses index 3, so the answer cubed returns the radicand.
What do the main Root Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Root Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Root Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
What do radicand and root index mean?
The radicand is the number inside the root. The root index tells which power to undo: index 2 is square root, index 3 is cube root, index 4 is fourth root, and so on.
Can this calculator handle negative numbers?
It can calculate real odd roots of negative numbers, such as root_3(-125) = -5. Even roots of negative numbers are not real numbers, so the calculator shows an error.
Why does an even root of a negative number fail?
In real numbers, an even power is never negative. That is why root_2(-16) and root_4(-81) do not have real-number answers on this page.
How are roots related to exponents?
A root can be rewritten as a rational exponent. The nth root of x is the same as x^(1/n).
How can I check a root answer?
Raise the answer to the root index. If root_5(32) returns 2, check it by calculating 2^5, which gives 32.
Why are some root answers decimals?
Some roots do not land on a whole number. For example, root_2(2) is about 1.41421356, so the calculator gives a decimal approximation.
Can the root index be a decimal?
No. This calculator uses positive whole-number root indexes of 2 or higher, such as 2, 3, 4, or 5.
Can I enter decimal radicands?
Yes. Decimal radicands work when the root has a real-number answer. The cube root of 0.008 is 0.2 because 0.2^3 = 0.008.
Is my root calculation history private?
Yes. Recent root answers stay only in the current browser tab while you use the page. They are not sent to a server.