Square Root Calculator
Enter a number and a root (2 for square root, 3 for cube root) and see the answer with a quick perfect-square check.
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The formula
The nth root of x is the number r such that r^n = x. Equivalent to x^(1/n).
What a square root is
The square root of a number is the value that gives the number back when you multiply it by itself. The square root of 144 is 12 because 12 x 12 = 144.
Numbers like 144, 81 and 25 are called perfect squares and have whole-number roots. Most numbers are not, so their roots go on forever without repeating. The square root of 2 is about 1.41421356 and never ends.
Cube roots and beyond
A cube root asks "what number multiplied by itself three times gives this?". The cube root of 27 is 3. Unlike square roots, cube roots work for negative numbers too: the cube root of -8 is -2.
Negative numbers
No real number multiplied by itself gives a negative, so the square root of -9 is not a real number. In maths it is written 3i, where i is the imaginary unit. The calculator shows that form so you are not left with an error.
Estimating by hand
Find the two perfect squares either side. For 50, 49 is 7 x 7 and 64 is 8 x 8, so the root is just over 7. A good first guess is 7.1, and the true value is about 7.07.
Examples to check
Type these into the calculator above to see how it behaves. Every result below was produced by the same calculator code that runs on this page.
| What you enter | What you get |
|---|---|
| Number: 144; Root (2 = square root, 3 = cube root): 2 | Square root: 12 |
| Number: 50; Root (2 = square root, 3 = cube root): 2 | Square root: 7.0710678119 |
| Number: 27; Root (2 = square root, 3 = cube root): 3 | Cube root: 3 |
| Number: 81; Root (2 = square root, 3 = cube root): 4 | 4th root: 3 |
Square Root Calculator: frequently asked questions
Is the square root always smaller than the number?
Only for numbers bigger than 1. The square root of 0.25 is 0.5, which is larger than 0.25.
Why is the square root of a number written with a plus or minus?
Because both 12 and -12 square to 144. The radical symbol means the positive (principal) root, which is the one this calculator returns.
How accurate is this calculator?
It uses standard double-precision arithmetic, accurate to about 15 significant digits. Results are rounded only for display.
Is what I enter in this calculator saved or sent anywhere?
No. The calculation runs in your browser, so what you enter is not sent to our servers. We only count, anonymously, whether a tool ran successfully.
Is this calculator free to use?
Yes. It is free, needs no sign-up and has no usage limit.
Last reviewed: October 3, 2026