Square Root Calculator
Find the square root of any number, plus the simplified radical form.
What the Square Root Calculator does
The square root of a number is the value that, multiplied by itself, gives that number. Every positive number has two square roots — one positive and one negative — though the radical symbol refers to the positive one.
Formula
√x = y where y² = xSimplify by extracting perfect square factors
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Number | number | Yes | Accepts 0 or more. |
How to use it
- Enter Number.
- Select Calculate.
Worked example
Find the square root of 72.
- Number
- 72
√72 ≈ 8.4853, and in radical form 6√2 because 72 = 36 × 2.
Reading the result
- Every positive number has two square roots, one positive and one negative, though the radical symbol refers to the positive one.
- A whole-number root means the input is a perfect square, which is what allows a radical to be simplified exactly.
Common mistakes
- Expecting a real answer from a negative input. Square roots of negatives are imaginary.
- Confusing the square root with halving. The square root of 16 is 4, not 8.
Frequently asked questions
What is the square root of a negative number?
It is imaginary. √−9 equals 3i, where i is the square root of −1. This calculator works in real numbers only.