Square Root Calculator

The square root of a number x is the value that, multiplied by itself, equals x. For example, the square root of 25 is 5, because 5 x 5 = 25. Every positive number has two square roots, one positive and one negative, but by convention the calculator returns the positive (principal) root.

Not with real numbers. The square root of a negative number is imaginary, written using i, where i x i = -1. This calculator only accepts non-negative inputs and returns no result for any value below zero.

A perfect square is an integer whose square root is also an integer. Common examples are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. The calculator flags these and shows the exact integer result instead of a decimal.

For a non-perfect-square integer, you can pull the largest perfect-square factor outside the radical sign. For example, sqrt(72) = sqrt(36 x 2) = 6 sqrt(2). The calculator shows this simplified form only when your input is a whole number; for decimals it shows the numeric result only.

The calculator uses JavaScript's built-in Math.sqrt(), which the language spec requires to return the correctly rounded result and which engines typically run as a hardware square-root instruction. By hand, you can estimate and refine: guess a value, square it, adjust up or down, and repeat until you reach the precision you need.

Approximately 1.414214 (rounded to 6 decimal places, this calculator's default). The exact value is irrational, so its decimal expansion continues forever without repeating and no fraction can represent it exactly.