Square Root Calculator
Find the square root of any number to 25 digits, and simplify roots like √72 = 6√2.
About the Square Root Calculator
The square root of x is the number that, multiplied by itself, gives x. Every positive number has two square roots (±); √ means the positive one. A root simplifies when the number has a perfect-square factor: √72 = √(36 × 2) = 6√2.
The formula
√(a² × b) = a√b
Perfect squares
| n | n² |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
Worked example
Example: √50 = 7.071067811865
- Input: Number: 50.
- Formula: √(a² × b) = a√b
- Find the largest perfect square factor 50 = 25 × 2
- Take its root outside √50 = 5√2
- Result: √50 = 7.071067811865
- Simplest radical form: 5√2
- 25 significant digits: 7.071067811865475244008444
- Is 50 a perfect square?: No
Questions people ask
What is the square root of 2?
1.4142135623730950488… It's irrational, so the digits never repeat.
Can a square root be negative?
x² = 25 has two answers, 5 and −5, but the √ symbol means the positive root, 5.