Root Calculator
Find the square root, cube root, or any nth root of a number.
Try an example
12
About this calculator
How This Root Calculator Works
Enter a number and a root degree (2 for square root, 3 for cube root, and so on), and the calculator returns the result.
The Formula
The nth root of a number is the value that, multiplied by itself n times, produces that number — calculated as number^(1/n). The square root of 144 is 12, because 12 × 12 = 144.
A Note on Negative Numbers
Even-degree roots (square root, 4th root, and so on) of a negative number aren't real numbers — there's no real number that, squared, gives a negative result. Odd-degree roots (cube root, 5th root) of a negative number do work, and return a negative result: the cube root of −27 is −3, since −3 × −3 × −3 = −27.
Worked example
The 2nd root (square root) of 144 is 12, since 12 × 12 = 144.
Frequently asked questions
What is the nth root of a number?
The value that, multiplied by itself n times, produces that number — it's calculated as number^(1/n).
Can I take the root of a negative number?
Only for odd-degree roots (like cube roots) — even roots (square, 4th, etc.) of a negative number aren't real numbers, so this calculator only returns a result for odd-degree roots of negative inputs.
What's the difference between a square root and a cube root?
A square root (degree 2) undoes squaring; a cube root (degree 3) undoes cubing — higher degrees follow the same pattern.
How is this related to exponents?
Taking the nth root is the same as raising a number to the power of 1/n.