Calculate the square root of any number instantly, or work backwards from a square root to find the original number. Enter either value and get the result on the fly.
What Is a Square Root?
The square root of a number x is the value y such that y × y = x. It is written as √x.
For example:
- √25 = 5, because 5² = 25
- √2 ≈ 1.4142, because 1.4142² ≈ 2
Every positive number has exactly two square roots — one positive and one negative — but by convention, √x refers to the positive (principal) square root.
How to Use This Calculator
Enter a number in either field:
- Number (x) — the calculator finds its square root
- Square Root (√x) — the calculator squares it to find the original number
The result updates as you type.
Square vs Square Root
These operations are inverses of each other:
| Operation | Symbol | Example |
|---|
| Square root | √x | √81 = 9 |
| Square | x² | 9² = 81 |
Perfect Squares
A perfect square is an integer whose square root is also a whole number.
| Number | Square root |
|---|
| 1 | 1 |
| 4 | 2 |
| 9 | 3 |
| 16 | 4 |
| 25 | 5 |
| 36 | 6 |
| 49 | 7 |
| 64 | 8 |
| 81 | 9 |
| 100 | 10 |
The calculator automatically notes when your number is a perfect square.
Sources
Frequently Asked Questions
What is a square root?
The square root of a number x is the value that, when multiplied by itself, gives x. For example, the square root of 25 is 5 because 5 × 5 = 25. It is written as √x.
How do you calculate a square root by hand?
For perfect squares (4, 9, 16, 25…), the square root is a whole number you can memorize. For other numbers, the most common hand method is the digit-by-digit (long division) method, or you can use the estimation method: guess a value, square it, adjust, and repeat. Most people use a calculator for non-perfect squares.
What are perfect squares?
A perfect square is an integer that is the square of another integer. The first ten perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their square roots (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) are all whole numbers.
Is the square root of 2 a rational number?
No. √2 ≈ 1.41421356… is an irrational number — its decimal expansion never repeats or terminates. This was proved by the ancient Greeks (attributed to Hippasus of Metapontum). Any square root of a non-perfect-square integer is irrational.
Is this calculator free?
Yes, completely free with no registration required.