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?
A square root of a number is a value that, multiplied by itself, gives that number. Because 5 x 5 = 25, the square root of 25 is 5, written as the square root of 25 = 5. Every positive number has two square roots, one positive and one negative, but "the" square root usually means the positive, or principal, root. A perfect square is a number whose square root is a whole number (1, 4, 9, 16, 25, and so on). This calculator finds the principal square root as a decimal and, for whole numbers, also gives the simplified radical form, and it handles other roots such as cube roots.
How to calculate and simplify a square root
For perfect squares the answer is exact: the square root of 144 is 12. For other numbers the root is irrational and shown as a decimal, for example the square root of 2 is about 1.414214. You can simplify a square root by pulling out the largest perfect-square factor: 72 = 36 x 2, and since the square root of 36 is 6, the square root of 72 = 6 times the square root of 2, about 8.485281. A cube root asks which number cubed gives the value, so the cube root of 27 is 3 because 3 x 3 x 3 = 27. Square roots of negative numbers have no real value, but cube roots of negatives do (the cube root of -8 is -2).
Example
To simplify the square root of 72, find the biggest perfect square that divides 72. That is 36, leaving 72 = 36 x 2. Take the root of the perfect square (the square root of 36 is 6) and leave the rest under the sign, giving 6 times the square root of 2. As a decimal that is about 8.485281.
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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.