√ Square Root Calculator

Find the square root, cube root, or any nth root of a number.

About this tool

Calculates the square root by default, but also handles cube roots and any other nth root by letting you set the root's index — a square root is simply the 2nd root, a cube root the 3rd, and so on.

Correctly handles negative numbers for odd roots (like cube roots, which do have real negative solutions) while flagging even roots of negative numbers as having no real result.

Worked example

The square root of 144 is 12. The cube root of −27 is −3.

How to use it

Enter the number you want the root of.
Enter the root index (2 for square root, 3 for cube root, etc.).
Press Calculate root.

Tips

A square root (index 2) only has a real result for numbers zero or greater — negative numbers under an even root require imaginary numbers, which this tool doesn't compute.
Cube roots (index 3) and other odd roots work fine with negative numbers — for example, the cube root of −8 is −2.
For the reverse operation — raising a number to a power instead of finding a root — use the Exponent Calculator.

FAQ

Why can't I take the square root of a negative number?

Any real number squared is positive or zero, so no real number squared gives a negative result — the square root of a negative number requires imaginary numbers, outside what this calculator computes.

Can I calculate a cube root of a negative number?

Yes — odd roots (3rd, 5th, 7th, etc.) of negative numbers have valid real solutions, and this tool computes them correctly.

What does the "root index" field mean?

It's which root you want: 2 for square root, 3 for cube root, 4 for fourth root, and so on — the standard mathematical notation is the small number written before the radical symbol.

From the blog: getting the most out of this tool

Square roots are the most common case by far, so that's the default — but we added the general nth-root field because cube roots come up often enough in geometry (volume-to-side-length problems) that a dedicated field felt worth the extra input box.

The negative-number handling here is a small detail that a lot of basic calculators get wrong or ignore — silently returning a nonsensical result instead of flagging that an even root of a negative number simply doesn't have a real answer.