Root calculator

What a root calculates

A root answers the reverse of an exponent question: "what number, multiplied by itself n times, gives me this result?" The square root of 64 is 8 because 8 × 8 = 64. The cube root of 64 is 4 because 4 × 4 × 4 = 64.

The formula this calculator uses

• ⁿ√x = x^(1/n) — the nth root of x equals x raised to the power of 1/n.
• For even-degree roots (square root, 4th root, etc.), negative numbers don't have a real result — the calculator will show an error in that case.
• For odd-degree roots (cube root, 5th root, etc.), negative numbers DO have a valid real result — for example, the cube root of -8 is -2.

Common roots at a glance

Square roots show up constantly in geometry (like finding a side length from an area) and statistics (like standard deviation). Cube roots come up when reversing volume calculations. Higher-degree roots are less common day-to-day but appear in engineering and finance formulas involving compound rates.