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.