We have seen square roots before, however, we will go into a bit more depth here. Also, we will generalize this concept and introduce nth roots. The definition of the principal (non-negative) square root follows.

**Simplify.**

Not all square roots work out so nicely. If trying to simplify a square root with a radicand that is not a perfect square, we can find the exact answer using the following properties.

Here

*A*and*B*are non-negative real numbers and*B*is not equal to zero. Approximations are made using a calculator.**Give the exact answer and approximate to the nearest hundredth.**

This idea can be extended to any positive integer index

*n.*
For 3rd roots, or cube roots, the question is “what raised to the 3rd power will produce the given number?" For example,

because

**Simplify.**

Remember that if the radicand of an odd root is negative then the result will be a negative real number. If the radicand of an even root is negative then the number is not real.

**Video Examples on YouTube:**