Square Root Calculator

Understanding Square Roots and Nth Roots

A square root is the inverse of squaring a number. If you square 5 to get 25, then the square root of 25 brings you back to 5. Written mathematically, √25 = 5. Square roots appear frequently in geometry (calculating distances and diagonals), physics (energy and wave equations), statistics (standard deviation), and finance (volatility calculations).

This calculator also computes cube roots and any nth root. The nth root of a number x is the value that, when raised to the nth power, equals x. The formula is: ⁿ√x = x^1/n. For example, the 4th root of 625 is 5 because 5&sup4; = 625. The cube root of 27 is 3 because 3³ = 27.

A perfect square is a number whose square root is a whole integer. The first twenty perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, and 400. Knowing whether a number is a perfect square is useful for simplifying radicals in algebra. For non-perfect squares, this calculator provides the result to full decimal precision. Negative numbers do not have real square roots, but this calculator will note when a result would be imaginary.