Square Root Calculator
The square root of any number — the value that multiplied by itself gives what you entered.
The square root of x is the number that squares to x, written √x.
How the square root calculator works
The square root of x is the number that squares to x, written √x. Every positive number has two square roots, one positive and one negative — √144 is 12, and −12 also squares to 144 — but the radical sign means the positive one, called the principal root. Perfect squares (1, 4, 9, 16, 25…) give whole answers; everything else gives an irrational decimal that never repeats.
Formula: ⁿ√x = x^(1/n)
Worked examples
| Inputs | Root | Note |
|---|---|---|
| √144 | 12 | 12 — a perfect square |
| √2 | 1.4142135624 | 1.41421… — irrational, the diagonal of a unit square |
| √1000 | 31.6227766017 | 31.6228 |
FAQFrequently asked questions
What is a square root?
The number that multiplied by itself gives yours: √49 = 7 because 7 × 7 = 49.
Does every number have two square roots?
Every positive number does — one positive, one negative. The √ sign means the positive one.
Can you square-root a negative number?
Not within the real numbers. It needs imaginary numbers, where √−1 is written i.
Which numbers are perfect squares?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and so on — the squares of the whole numbers.
Why is √2 irrational?
Because no fraction squares to exactly 2 — a fact the Greeks proved and reportedly found deeply unwelcome.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.