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08 Jun 2023, 07:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (01:49) correct
32%
(01:38)
wrong
based on 558
sessions
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If \(a=\sqrt{√\frac{1}{5}+√\frac{1}{3}-√\frac{1}{2}}\), \(b=\sqrt{√\frac{1}{5}-√\frac{1}{3}+√\frac{1}{2}}\), \(c=\sqrt{-√\frac{1}{5}+√\frac{1}{3}+√\frac{1}{2}}\), which of the following is true?
A. a < c < b
B. a < b < c
C. c < b < a
D. c < a < b
E. b < a < c
A. a < c < b
B. a < b < c
C. c < b < a
D. c < a < b
E. b < a < c
08 Jun 2023, 08:29
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Root(5) > Root(2) implies 1/root(2) > 1/root(5)
Therefore 1/root(2) > 1/root(3) > 1/root(5)
I think its B -->>
a < b < c
Therefore 1/root(2) > 1/root(3) > 1/root(5)
I think its B -->>
a < b < c
19 Jun 2023, 05:59
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Bunuel
We don't have to calculate too much for solving this. There's a simpler explanation by extreme oversimplification
. Thankfully the numbers in the question stem are the same and the only difference is whether the number is positive or negative. We can ignore the roots and just work with decimals to get an approximation, eg.
\(√\frac{1}{5}\) can be 0.2 .....(Root of this number will still be the smallest amongst 3)
\(√\frac{1}{3}\) can be 0.33 .....(Root of this number will still be the middle value)
\(√\frac{1}{2}\) can be 0.5 .....(Root of this number will still be the largest amongst 3)
So I can approximate \(a=\sqrt{√\frac{1}{5}+√\frac{1}{3}-√\frac{1}{2}}\) as 0.2+0.33-0.5 = 0.03
\(b=\sqrt{√\frac{1}{5}-√\frac{1}{3}+√\frac{1}{2}}\) as 0.2-0.33+0.5 = 0.37
\(c=\sqrt{-√\frac{1}{5}+√\frac{1}{3}+√\frac{1}{2}}\) as -0.2+0.33+0.5 = 0.63
So, a < b < c
Thus option C
