Square Root & Nth Root Calculator

Find a square root, cube root or any root up to the 10th — simplified exactly (like √72 = 6√2), with the decimal.

Whole numbers, decimals or fractions such as 2/3

Result

Enter values and press Calculate to see the result.

Formula

a2b=ab\sqrt{a^2 b} = a\sqrt{b}

Take square factors out of the root: √72 = √(36 × 2) = 6√2.

anbn=abn\sqrt[n]{a^n b} = a\sqrt[n]{b}

For an nth root, take out factors that are perfect nth powers.

How to use this calculator

  1. Enter the number and choose which root you want.
  2. Press Calculate to get the simplified exact root and its decimal value.

Worked example

The square root of 72

72 = 36 × 2, and 36 = 6² is a perfect square.

√72 = √(6² × 2) = 6√2 ≈ 8.485281.

Frequently asked questions

Why is the answer written as 6√2 instead of a decimal?

√2 never ends or repeats, so 6√2 is the exact answer. The decimal shown with it is rounded.

Can I take the root of a negative number?

Odd roots, yes: ∛(−27) = −3. Even roots (square, 4th, …) of a negative number are not real numbers.