Square Root and Nth Root Calculator

Find the square root, cube root, and nth root of any number at once. Supports real roots of negative numbers with odd indices, with a graph.

Input

Enter a number x and an index n to compute the nth root, which is x to the power of 1 over n. The square root and cube root are shown as well.

Number x

The number to take the root of. Negative numbers are allowed.

Index n

The degree of the root. Use 2 for the square root and 3 for the cube root.

The 2th root of x

Square root

Cube root

2.5198421

Nth root

Check (nth root to the 2th power)

When x is negative, a real root exists only when the index n is odd. For an even index the result is shown as no real root.

The nth root is defined as x raised to the power of 1 divided by n. Raising it to the nth power returns the original number x.
When the index n is 2 the result is the square root, and when n is 3 it is the cube root.
For a positive x the calculator returns the positive real root. When x is 0 the root is also 0.
When x is negative a real root exists only when the index n is odd, and that value is negative. For example, the cube root of minus 8 is minus 2.
When x is negative and the index n is even, no real root exists, so the result is shown as no real root.
The verification field shows the nth root raised back to the nth power, which in theory equals the x you entered.

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