Is -10 a square root of 100?

Answer 1

In some sense, yes. However, due to standard mathematical notation, the square root of 100 is 10. There are some things to note. First, when we use a square root sign (or any root sign) in math, it is assumed we mean the principal root. This is the root that is greater than or equal to 0. The principal root of 100 is 10, so when asked just for the square root of 100, it is generally assumed the answer is simply 10.

To be more complete, when taking all second roots of 100 (all square roots), we get 10 and -10. The number -10 is a second root of 100, just not the principal root.

Finally, when considering equations such as x2 = 100, we must take the positive and negative square roots of 100 (the principal root and inverse of the principal root) to find all the solutions. We get x = 10, -10.