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# If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?

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Manager
Joined: 02 Dec 2012
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If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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12 Dec 2012, 08:32
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91% (01:32) correct 9% (00:53) wrong based on 992 sessions

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If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39723
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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12 Dec 2012, 08:33
1
KUDOS
Expert's post
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

$$\sqrt{\frac{r}{s}}=s$$ --> $$\frac{r}{s}=s^2$$ --> $$r=s^3$$.

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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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24 Jan 2015, 17:59
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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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24 Jan 2015, 19:05
Expert's post
1
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BOOKMARKED
Hi All,

This question can be solved by TESTing VALUES. The key is to keep the values relatively small and think about how the square root sign impacts the math:

We're told that S > 0 and (r/s)^1/2=s

We're asked for the value of R.

IF....
R = 8
S = 2
\sqrt{4} = 2

So we're looking for an answer that = 8 when S = 2....

Answer A: 1/2 NOT a match
Answer B: \sqrt{2} NOT a match
Answer C: 2\sqrt{2} NOT a match
Answer D: 2^3 = 8 This IS a MATCH
Answer E: 2^2 - 2 = 2 NOT a match

[Reveal] Spoiler:
D

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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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11 Jun 2016, 06:41
Expert's post
1
This post was
BOOKMARKED
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

To solve, we need to simplify the equation √(r/s) = s.

We first want to eliminate the square root, so we square both sides, obtaining:

(√(r/s))^2 = s^2

r/s = s^2

To isolate r, we multiply the entire equation by s and we get:

r = s^3

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Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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12 Jun 2016, 05:10
If s > 0 and $$\sqrt{\frac{r}{s}}=s$$, what is r in terms of s ?

(A) 1/s
(B) $$\sqrt{s}$$
(C) $$s\sqrt{s}$$
(D) s^3
(E) s^2-s

An alternate method will be testing the options , except (D) none follows -

$$\sqrt{\frac{s^3}{s}}=\sqrt{s^2}$$ = $$s$$
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Manager
Joined: 03 Jan 2017
Posts: 201
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? [#permalink]

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25 Mar 2017, 11:49
let's pick smart numbers and solve: let s be 3, then r is 27
if we test the answers D is the only that works
Re: If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?   [#permalink] 25 Mar 2017, 11:49
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