If s>0 and √(r/s) = s, what is r in terms of s?
A) 1/s
B) √s
C) s√s
D) s³
E) s² - s
I would recommend straight algebra:
( √(r/s) )² = s²
r/s = s²
r = s³.
The correct answer is
D.
An alternate approach is to plug in an easy value for s and solve for r.
If s=2, we get:
√(r/2) = 2.
Since √4 = 2, the value under the square root -- r/2 -- must be equal to 4:
r/2 = 4.
r = 8. This is our target.
Now we plug s=2 into the answer choices to see which yields our target of 8.
Only
D works:
s³ = 2³ = 8.
For this problem, algebra seems easier and more efficient.
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