How it works
The nth root of x is the number that, multiplied by itself n times, gives x. The square root of 144 is 12 because 12 × 12 = 144; the cube root of 27 is 3 because 3 × 3 × 3 = 27.
For whole numbers that are not perfect powers, the calculator also gives the simplified radical. It pulls out every factor that appears n times: √72 = √(36 × 2) = 6√2.
Odd roots of negative numbers are real (∛−8 = −2). Even roots of negative numbers are imaginary and are not calculated here.
Formula
ⁿ√x = x^(1/n)
Questions people ask
How do I simplify a square root?
Find the largest perfect square that divides the number and take its root outside. √50 = √(25 × 2) = 5√2.
Does a square root have two answers?
The equation x² = 16 has two solutions, 4 and −4, but the square root symbol √16 means the principal (non-negative) root, 4.
What is the square root of a negative number?
It is imaginary. √−9 = 3i, where i is defined by i² = −1.