Square Root Calculator
Find the square root of a number as a decimal and in simplified radical form. Switch the root degree for cube roots and other nth roots.
Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026
Result
8.48528
Simplified radical: 6√2
Perfect square: No
What is a square root?
The square root of a number is the value that, multiplied by itself, gives that number. For example, the square root of 9 is 3, because 3 × 3 = 9. Every positive number has two square roots, one positive and one negative, but the "principal" square root — the one this calculator shows — is the positive value. The symbol for a square root is the radical sign √.
How square roots are calculated
A perfect square such as 144 has a whole-number root (√144 = 12). When a number is not a perfect square, its root is an irrational decimal, but it can often be simplified by pulling out the largest perfect-square factor. For example, 72 = 36 × 2, so √72 = √36 × √2 = 6√2. A fractional power is the general form: the cube root is the power ⅓, and the nth root is the power 1/n.
Example
√144 = 12 exactly, because 144 is a perfect square. √72 is about 8.485, which simplifies to 6√2. The cube root of 27 is 3, because 3 × 3 × 3 = 27.
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Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer
How to use
Enter a number and a root degree (default 2 for square root). The calculator shows the principal nth root as a decimal.
For square roots it also shows whether the number is a perfect square and the simplified radical form. Even roots of negative numbers are flagged as having no real solution.