Find the nth root of a number — square, cube, or any index. Enter the number and the root index.
Usage Tip
A fractional exponent is a root: x^(1/3) is the cube root, x^(2/3) is the cube root squared.
The inverse of raising to the power n
Even roots of negative numbers are not real; odd roots are.
The check column raises the result back to the power n to confirm.
Even roots require a non-negative number.
The nth root of a number is the value that, multiplied by itself n times, gives the original number. The square root uses an index of 2 and the cube root uses an index of 3. It is the same as raising the number to the power of one over n, so the cube root of 27 is 3 because 3 times 3 times 3 is 27.
Even roots of negative numbers are not real, because no real number multiplied by itself an even number of times gives a negative result. Odd roots of negative numbers work fine, so the cube root of minus 8 is minus 2. Roots are used to find side lengths from areas and volumes, geometric means, and the growth rate in compound growth problems.