Square Root Calculator — √n, ³√n, ⁿ√x

The square root of a number n is the value x such that x² = n. For example, √25 = 5 because 5² = 25. Every positive number has two square roots: positive and negative. We typically refer to the principal (positive) root.

A perfect square is an integer that is the square of another integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their square roots are whole numbers.

To simplify √n, find the largest perfect square factor of n. For example, √48 = √(16×3) = 4√3. The simplified form has the largest perfect square taken outside the radical.

The cube root of n (written ³√n) is the value x such that x³ = n. For example, ³√27 = 3 because 3³ = 27. Unlike square roots, cube roots exist for negative numbers: ³√(-8) = -2.

In real numbers, negative numbers do not have real square roots. However, in complex numbers, √(-1) = i (the imaginary unit). For example, √(-9) = 3i.