Square roots appear in geometry, physics and statistics, from the Pythagorean theorem to standard deviation.
How to use the Square Root Calculator
- Number
- Want to work backwards? Type a value into Square root and Number is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
The calculator raises x to the power one half. Negative inputs have no real square root.
What each result means
- Square root = sqrt([Number])
- Cube root = cbrt([Number])
Example values
How the main result changes when Number changes and everything else stays at the example values above:
| Number | Square root |
|---|---|
| 25 | 5 |
| 37.5 | 6.1237 |
| 50 | 7.0711 |
| 62.5 | 7.9057 |
| 75 | 8.6603 |
| 100 | 10 |
Formula
√x = x^(1/2)Worked example
Inputs — Number: 50.
Results — Square root = 7.07106781; Cube root = 3.6840315; Perfect square? = 0.
Key terms
- Perfect square
- A number whose square root is a whole number.
Frequently asked questions
What is the square root of a negative number?
It is imaginary; for example √−9 = 3i.
How do I simplify √50?
50 = 25 × 2, so √50 = 5√2 ≈ 7.071.
What formula does the Square Root Calculator use?
√x = x^(1/2).
Can I work backwards from the result?
Yes. Type the result you want into Square root and the calculator finds the matching number.