Math & Stats

Square Root Calculator

Find the square root or any nth root of a number instantly. This free Square Root Calculator also detects perfect squares and perfect cubes.

Square Root Calculator

Number (x)

Root Degree (n)

Method

How this calculator works

The nth root of x is x^(1/n). For a real result: if x is negative and n is odd, the root is -(|x|)^(1/n); if x is negative and n is even, no real root exists. A perfect square or cube occurs when the root is a whole number.

Enter the number (x) you want to take the root of.
Enter the root degree (n); leave it at 2 for a standard square root.
For a negative x, use an odd root degree — even roots of negatives are not real.
Click Calculate or edit a field to recompute automatically.
The tool shows the root value and flags perfect squares or perfect cubes.

Examples

Worked examples

Real numbers, end-to-end results.

√144 (n = 2)

144 is a perfect square because 12 × 12 = 144.

Cube root of 27 (n = 3)

27 is a perfect cube because 3 × 3 × 3 = 27.

Cube root of -8 (n = 3)

-2

An odd root degree allows a real root of a negative number.

Use cases

When to use it

Solving geometry problems involving areas, diagonals, and the Pythagorean theorem.
Simplifying radicals and checking algebra homework.
Finding side lengths from area or volume in construction and design.
Evaluating standard deviation and other statistics that use square roots.

FAQ

Frequently asked questions

What is a square root?

The square root of a number x is the value that, when multiplied by itself, gives x. For example, the square root of 144 is 12 because 12 × 12 = 144.

What is an nth root?

An nth root of x is a number that, raised to the power n, equals x. The cube root (n = 3) of 27 is 3 because 3³ = 27. Set the root degree field to choose n.

Can you take the root of a negative number?

Only with an odd root degree. The cube root of -8 is -2, but an even root such as the square root of -4 has no real value, so the calculator shows an error.

What is a perfect square?

A perfect square is an integer that is the square of another integer, such as 1, 4, 9, 16, and 25. This tool flags results like √144 = 12 as perfect squares.

How accurate are the results?

The calculator uses IEEE 754 double-precision floating-point math, so results are accurate to about 15 significant digits and are rounded neatly for display.