Square Root Calculator
Square root, cube root and any nth root of a number.
Quick answer
- Formula: √x = x^(1/2); nth root = x^(1/n)
- Worked example — Square root (√): 12.0000 (full example below).
Square Root Calculator
| Square root (√) | 12.0000 |
| Cube root (∛) | 5.2415 |
| Nth root | 12.0000 |
√144 = 12 exactly, because 144 is a perfect square (12²). Its cube root is about 5.2415, since 5.2415³ ≈ 144.
The square root of a number is the value that, multiplied by itself, gives the number back: √144 = 12 because 12 × 12 = 144. Cube roots do the same with three multiplications, and nth roots generalize the idea.
Enter a non-negative number and a root degree. You get the square root, the cube root and the root of the degree you chose — handy for geometry, where side lengths come from areas and volumes via roots.
The formula
Worked example
√144 = 12 exactly, because 144 is a perfect square (12²). Its cube root is about 5.2415, since 5.2415³ ≈ 144.
The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.
Frequently asked questions
Which numbers have exact square roots?
Perfect squares: 1, 4, 9, 16, 25, 36 and so on. Every other non-negative number has an irrational square root — √2 ≈ 1.4142… continues forever without repeating.
Why can't I take the square root of a negative number here?
No real number squared gives a negative result, so square roots of negatives belong to the complex numbers (written with i). This calculator works in real numbers only and will ask for a non-negative input.
Category: Math calculators
Sources & methodology
This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.
Content last reviewed by CalcHub Editorial.
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