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.
If m and n are positive integers, each of the following...
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Equate each option equal to √(800mn)
And Find the value of n.
You will find that you get an integer in every case except for option D where you get n = 5/2
Hence D is the correct option
And Find the value of n.
You will find that you get an integer in every case except for option D where you get n = 5/2
Hence D is the correct option
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√(800mn) = √100 x √8 x √(mn) = 10 x 2√2 x √(mn) = 20√(2mn)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.
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
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