Square Root Calculator

The square root of a number x is a value y such that y² = x. For example, √144 = 12 because 12² = 144. Every positive number has two square roots (positive and negative), but we conventionally report the positive (principal) root.

Most square roots are irrational — they cannot be expressed as a simple fraction and their decimals go on forever without repeating. √2 = 1.41421356... Perfect squares (1, 4, 9, 16, 25...) have exact integer square roots.

Numbers whose square roots are whole integers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400... The square root of a perfect square is always an integer.

Factor out perfect squares. Example: √72 = √(36×2) = 6√2. Find the largest perfect square factor, take its root, and leave the remainder under the radical.

They are identical. √x = x^(1/2) = x^0.5. Similarly, cube root = x^(1/3). This is why calculators use the ^ operator for roots as well as powers.