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# If x > 0 and y >0

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If x > 0 and y >0 [#permalink]  22 Mar 2018, 03:25
Expert's post
00:00

Question Stats:

87% (00:50) correct 12% (00:08) wrong based on 16 sessions
If $$x > 0$$ and $$y > 0$$, which of the following is equivalent to $$\frac{x}{y} \sqrt{\frac{y}{x^2}$$?

(A) $$1$$

(B) $$\frac{\sqrt{x}}{\sqrt{y}$$

(C) $$\sqrt{x}$$

(D) $$\frac{1}{\sqrt{x}$$

(E) $$\frac{1}{\sqrt{y}$$
[Reveal] Spoiler: OA

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Re: If x > 0 and y >0 [#permalink]  22 Mar 2018, 05:41
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I forgot how much I hate simplifying square roots...

(x/y)(\sqrt{(y/x^2)}

First we square it so we can get rid of the square root:

((x/y)(\sqrt{(y/x^2)})^2
(x^2/y^2)(y/x^2)

Now we multiply and cancel out equal terms:

((x^2)y)/(y^2)(x^2))
1/y

Because we had to square it to get rid of the sqaure root now we have to sqaure root this result giving us 1/\sqrt{y}
Founder
Joined: 18 Apr 2015
Posts: 6898
Followers: 114

Kudos [?]: 1342 [0], given: 6309

Re: If x > 0 and y >0 [#permalink]  22 Mar 2018, 12:51
Expert's post
if you wrap up the LaTex code with the  tags the result will be more efficient

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Re: If x > 0 and y >0 [#permalink]  10 Apr 2019, 09:16
1
KUDOS
Carcass wrote:
If $$x > 0$$ and $$y > 0$$, which of the following is equivalent to $$\frac{x}{y} \sqrt{\frac{y}{x^2}$$?

(A) $$1$$

(B) $$\frac{\sqrt{x}}{\sqrt{y}$$

(C) $$\sqrt{x}$$

(D) $$\frac{1}{\sqrt{x}$$

(E) $$\frac{1}{\sqrt{y}$$

Here

$$\frac{x}{y} \sqrt{\frac{y}{x^2}$$ can also be written as = $$\sqrt{\frac{(x^2) y}{(y^2) (x^2)}$$ = $$\frac{1}{\sqrt{y}$$
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Re: If x > 0 and y >0   [#permalink] 10 Apr 2019, 09:16
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