Square Root Calculator
The square root of a number is the value that, multiplied by itself, gives that number. Enter any number to get its square root, its cube root and its square — and whether it is a perfect square.
Your numbers
Result
- Cube root
- 5.24
- Squared (n²)
- 20,736
- Perfect square
- Yes
| Operation | Value |
|---|---|
| Square root √144 | 12 |
| Cube root ∛144 | 5.24148279 |
| Squared 144² | 20736 |
| Perfect square? | Yes |
What a square root is
√n is the number that squares to n: √144 = 12 because 12 × 12 = 144. Perfect squares (1, 4, 9, 16, 25, …) have whole-number roots; most numbers do not, so √2 ≈ 1.414 runs on forever. Every positive number has two square roots (+ and −); this returns the principal (positive) one.
Roots and powers
A square root is the same as raising to the power ½: √n = n^0.5. The cube root ∛n undoes cubing (∛27 = 3). Roots and powers are inverse operations — squaring then square-rooting returns the original number, which is why the calculator shows n² alongside the roots.
Negative numbers
A negative number has no real square root, because no real number squared is negative — that is where imaginary numbers come in (√−1 = i). This calculator works with real numbers, so a negative input has an undefined square root. The cube root of a negative number is real, though: ∛−27 = −3.
Frequently asked questions
Sources
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