kaplan roots

Just to clarify the question, the whole thing is under the root sign.

In other words, it's:

root ((4*9 + 9*16)/25)

We know that root (a/b) = roota/rootb. So, our first step in simplifying is to rewrite the expression as:

root(4*9 + 9*16)/root25 = root(4*9 + 9*16)/5 = root(36 + 144)/5

Choice (a) is a common trap designed for people who don't fully understand explonent/root rules. Here are the basics:

roota * rootb = root(ab)
roota/rootb = root(a/b)

HOWEVER:

roota + rootb does NOT= root(a+b)
and
roota - rootb does NOT= root(a-b)

So, we CANNOT say that root(36 + 144) = root36 + root144 = 6 + 12 = 18.

The proper way to solve is to add them together THEN take the root.

So:

root(36 + 144)/5 = root180/5 = root(36*5)/5 = root36*root5/5 = 6root5/5: choose (e).