### Square root problem

prove that

5√20 × √45 × √5 = 150√5

This is a quite easy problem. You use two basic "ideas" or properties relating to square roots:

* that √b × b is b - or that you can "pull out" a number times itself from under the root (this is just the definition of a square root of course).

* that √a √b = √ab - or you can combine the radicands under the same root when they are multiplied.

So √20 * √45 is equal to √20*45 = √4 × 5 × 5 × 9

= √2 × 2 × 5 × 5 × 3 × 3 = 2 × 5 × 3 = 30.

So that's the crux of that problem.