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Root Calculator

Calculate the nth root of any number, from square roots to higher degrees.
2 = square root, 3 = cube root.
ⁿ√x
12
Value

144

Degree

2

Check (resultⁿ)

144

Formula
ⁿ√x = x^(1/n); for x < 0 with odd n, ⁿ√x = −(−x)^(1/n)

About this calculator

The nth root of a number x is the value that, raised to the power n, gives back x. The square root (n = 2) and cube root (n = 3) are the most common cases. Roots are the inverse operation of exponentiation.

For non-negative values the nth root is x^(1/n). Negative values have a real root only when n is an odd integer, in which case the result is negative. Even roots of negative numbers are not real, so the calculator flags those inputs.

Frequently asked questions

Not within the real numbers. The square root of a negative number is imaginary, so this real-valued calculator does not return a result for it.

It is negative. For example, the cube root of −27 is −3, because (−3)³ = −27. Any odd root of a negative number is defined and negative.

Taking the nth root is the same as raising to the power 1/n, so the cube root of 8 equals 8^(1/3) = 2.

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