Enter a number and the root degree to find its n-th root.
Roots as the reverse of powers
A root undoes an exponent. The square root of a number is the value that, multiplied by itself, returns that number, and the cube root is the value multiplied by itself three times. In general the n-th root asks which number raised to the n-th power gives your input.
One rule trips people up: you cannot take an even root of a negative number and get a real result, because squaring any real number produces a positive value. Odd roots of negatives are fine and come out negative.
The formula
Worked example
The cube root of 27 is 27 ^ (1 / 3) = 3.
How to read your result
Even roots of negative numbers have no real value, since no real number squared is negative. Odd roots of negative numbers are negative and real.
Frequently asked questions
- What is the n in the n-th root?
- It is the degree: 2 for square root, 3 for cube root, and so on.
- Why does a negative number have no even root?
- Because squaring any real number gives a positive result.
- Is a root the same as a fractional exponent?
- Yes, the n-th root equals raising to the power one over n.
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