BTGmoderatorLU wrote:If m and n are positive integers, each of the following could be equivalent to,
$$\sqrt{800mn}\ Except.$$

$$A.\ \ 80\sqrt{m}$$
$$B.\ \ 40\sqrt{10m}$$
$$C.\ \ 40m\sqrt{5}$$
$$D.\ \ 20\sqrt{5m}$$
$$E.\ \ 20\sqrt{2m}$$

The OA is D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

√(800mn) = √100 x √8 x √(mn) = 10 x 2√2 x √(mn) = 20√(2mn)

We can go over the given answer choices one by one; however, since both D and E have 20 as a coefficient of the square root, as does our simplified expression, let's check those two choices first.

If 20√(5m) in choice D equals 20√(2mn), we must have:

√(5m) = √(2mn)

5m = 2mn

5 = 2n

2.5 = n

However, we are given that n is a positive integer, so n can't be 2.5. In other words, 20√(5m) can't be equivalent to √(800mn). (We see that there is no need to check choice E or any other choices.)

Answer: D