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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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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, 07:32
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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

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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 Dec 2012, 07:33
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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

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

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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, 16:59
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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, 18:05
Expert's post
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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, 05:41
Expert's post
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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

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, 04:10
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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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, 10:49
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

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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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30 Aug 2017, 13:32
Expert's post
Top Contributor
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

Let's test some values that satisfy the given equation √(r/s) = s

For example, r = 125 and s = 5 satisfies the equation √(r/s) = s

What is r in terms of s ?
Check the answer choices to see which one yields 125 when s = 5

(A) 1/5125 ELIMINATE
(B) √5125 ELIMINATE
(C) 55125 ELIMINATE
(D) 5^3 = 125 KEEP!!
(E) 5^2 - 5125 ELIMINATE

[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] 30 Aug 2017, 13:32
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