Square Root & Root Calculator

Formula used

The nth root of x is x^(1/n); the square root is the special case n = 2

How to use this calculator

1. Enter the number you want the root of.
2. Leave the degree at 2 for a square root, or set 3 for a cube root and so on.
3. Odd roots of negative numbers are supported; even roots of negatives are not real.

Example calculation

What does this result mean?

A square root answers 'what number multiplied by itself gives this?'. Every positive number has two square roots, one positive and one negative; the principal root shown here is the positive one. Roots of non-perfect squares are irrational, meaning their decimal expansion never repeats — the displayed value is rounded.

Frequently asked questions

Why do calculators show only the positive root?

By convention the radical symbol denotes the principal, non-negative root. In an equation such as x² = 9 you must include both +3 and −3.

Can I take the root of a negative number?

Odd roots yes — the cube root of −8 is −2. Even roots of negatives are complex numbers rather than real ones.

How do I estimate a square root mentally?

Find the nearest perfect squares either side. √50 sits between √49 = 7 and √64 = 8, and much closer to 7 — about 7.07.

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