In my first week of Precalc 11 we did a lot of review from previous years, but one new thing that I learned was about mixed and entire radicals. An entire radical is when you have a coefficient of  1 (the one is invisible so you don’t have to write it in front), and a mixed radical is when there is a coefficient that is a number higher than 1. Mixed radicals are the simplified version of  an entire radical. Some mixed radicals can be turned into entire radicals and entire radicals can be turned into mixed radicals, but not all. The radicand has to be a number that is a perfect square for it to be changed from entire to mixed radical.

In the photo I included below I broke it down and wrote out the steps on how to change from an entire radical to a mixed radical and a mixed radical to an entire radical. I also included examples of entire radicals that cannot be changed into mixed radicals.