Square Root and Nth Root Calculator

Calculate square roots, cube roots, and any nth root of a number with precision.

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1. Enter the number (radicand) you want to find the root of. 2. Select the root degree: square root, cube root, or enter a custom nth root. 3. View both the exact result and decimal approximation. 4. Check the perfect power indicator to see if the result is a whole number. 5. Review the simplified radical form if applicable. 6. Click the copy button to copy any result.

About This Tool

The Square Root and Nth Root Calculator computes roots of any degree for any positive number. Enter a number and the degree of the root (2 for square root, 3 for cube root, or any positive integer for higher roots), and get the result instantly. The tool displays both the exact result (when it is a perfect root) and a high-precision decimal approximation.

Square roots and cube roots are among the most commonly needed mathematical operations. From calculating distances using the Pythagorean theorem to determining the side length of a square with a known area, roots appear constantly in geometry, physics, engineering, and everyday problem-solving. Higher-order roots are used in statistics, finance, and advanced mathematics.

The calculator also identifies perfect squares, perfect cubes, and other perfect powers, letting you know when the result is an exact integer. For non-perfect roots, it provides the simplified radical form when possible (for example, the square root of 50 as 5 times the square root of 2) alongside the decimal approximation.

Formula / How It Works

nth root of x = x^(1/n) | Square root of x = x^(1/2) | Cube root of x = x^(1/3)

Frequently Asked Questions

The square root of a number x is a value that, when multiplied by itself, gives 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 we usually refer to the positive one.
A perfect square is a number whose square root is a whole number. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. The square root of a perfect square is always an integer.
Not in real numbers. The square root of a negative number is an imaginary number. For example, the square root of -1 is defined as "i" (the imaginary unit). This calculator works with positive real numbers.
Unlike square roots, cube roots of negative numbers are real. The cube root of -27 is -3 because (-3) x (-3) x (-3) = -27. Odd-degree roots of negative numbers always produce negative results.
The nth root of x is the same as x raised to the power of 1/n. For example, the cube root of 8 = 8^(1/3) = 2. This relationship connects roots to the broader rules of exponentiation.

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