Square Root Calculator

Find √ of any non-negative number, plus perfect-square detection and nearby roots.

Enter your details and press Calculate to see results.

Formula

√x is the number y where y × y = x

Example

√144 = 12 because 12 × 12 = 144.

Estimating square roots mentally

Bracket the number between perfect squares you know. √50 sits between √49 (7) and √64 (8), much closer to 7 — about 7.07. This estimate is accurate enough for quick checks.

Where square roots appear

Geometry (diagonals and the Pythagorean theorem), physics (distance fallen), finance (volatility) and statistics (standard deviation) all lean on square roots.

Frequently asked questions

What is the square root of a negative number?

Real square roots require non-negative inputs; negatives involve imaginary numbers (√−1 = i). This calculator works with real numbers only.

What is a perfect square?

The square of an integer: 1, 4, 9, 16, 25 and so on. Their roots are always whole numbers.