How is multiplying radicals so similar to just simplifying them?

Lets take a look at an example:

sqrt (45) can be written as the product of sqrt (9) and sqrt (5). Since the sqrt (9) = 3, the product becomes 3 (sqrt (5)). When radicals are simpified, the perfect squares are factored out inside of the radical. sqrt (45) can be written as sqrt (9*5) since sqrt (9) = 3, the result then becomes 3sqrt (5). They are similar because the same steps are taken with multiplying radicals as when radicals are simplified.