It is possible to take the square root of a negative number, but you don't get a real number.
If you can write the number whose square root you want as the product of two equal factors, the square root of that number will be one of those factors. For example, 4 = 2*2, so the square root of 4 is 2. Every positive number has two square roots: a positive square root and a negative square root. The symbol √n is taken to mean the principal or positive square root. The cube root of a number (positive or negative) is one of three equal factors of that number, so 3√27=3, since 27 = 3*3*3. Similarly, 3√−8=−2 since -8 = (-2)(-2)(-2). Real numbers have only 1 real cube root.
Source: https://www.physicsforums.com/threads/square-root-and-cube-root-question.375003/
These aren't my words!! I just copied and pasted, since I honestly had no idea either. :) It's been a while! Hopefully this helps
