I get confused only at the very end of this problem...I got the answer from the book:

= 5 *3 - 2 *3
=(5 - 2) *3
= 3 *3

My question is: where does the other *3 go? Why is there only one *3 in the final answer?

2. $5\sqrt{3} - 2\sqrt{3} = 3\sqrt{3}$

Imagine $a = \sqrt{3}$: $5a - 2a = 3a$

3. Originally Posted by endlesst0m
My question is: where does the other *3 go? Why is there only one *3 in the final answer?
The answer is: it's still there! You start off with two square roots of three being subtracted from five square roots of three. You are then left with three square roots of three, because 5 of something minus 3 of something is 2 of that something.

There may only be one radical in the final answer, but it is being multiplied by three, which is the same as adding it to itself twice.