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The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =

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SVP
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Status: The Best Or Nothing
Joined: 27 Dec 2012
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The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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New post 30 Dec 2014, 23:10
2
1
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (02:22) correct 25% (02:25) wrong based on 63 sessions

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The expression \((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2 =\)

A) 21
B) 20
C) 19
D) 18
E) 17

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The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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New post 31 Dec 2014, 01:04
Wow. That is a tough one, when you think about the time constraint in the GMAT. The correct answer is D.

First we carry out the sum:

\((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2 = (\frac{1\sqrt{8 +\sqrt{63}}}{\sqrt{8 - \sqrt{63}}\sqrt{8 +\sqrt{63}}} +\frac{1\sqrt{8 -\sqrt{63}}}{\sqrt{8 +\sqrt{63}}\sqrt{8 -\sqrt{63}}})^2\)

Then we can simplify the denominators:

\(=(\frac{\sqrt{8 +\sqrt{63}}}{\sqrt{(8 - \sqrt{63})(8 +\sqrt{63})}}+\frac{\sqrt{8 -\sqrt{63}}}{\sqrt{(8 - \sqrt{63})(8 +\sqrt{63}}})^2=(\frac{\sqrt{8 +\sqrt{63}}}{\sqrt{64-63}}+\frac{\sqrt{8 -\sqrt{63}}}{\sqrt{64-63}})^2=(\frac{\sqrt{8 +\sqrt{63}}+\sqrt{8 -\sqrt{63}}}{1})^2\)

Now we carry out the square:

\(=8+\sqrt{63}+8-\sqrt{63}+2\sqrt{8 +\sqrt{63}}\sqrt{8 -\sqrt{63}}=16+2\sqrt{64-63}=18\)

Given the time you could waste on this question and the fact that you can't really guess strategically because the answer choices are so close together, it is probably best to skip such a question unless you are 100% sure you can afford a loss of a few minutes when you come across this question.
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Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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New post 31 Dec 2014, 02:52
2
2
Easy method:

\((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2\)

Multiply \(\frac{1}{\sqrt{8 - \sqrt{63}}} * \frac{\sqrt{8 + \sqrt{63}}}{\sqrt{8 + \sqrt{63}}} = \sqrt{8 + \sqrt{63}}\)

similarly\(\frac{1}{\sqrt{8 +\sqrt{63}}} * \frac{\sqrt{8 - \sqrt{63}}}{\sqrt{8 - \sqrt{63}}} = \sqrt{8 - \sqrt{63}}\)

\(= (\sqrt{8 + \sqrt{63}} + \sqrt{8 -\sqrt{63}})^2\)

\(= 8 + \sqrt{63} + 2 * \sqrt{(8 + \sqrt{63})(8 - \sqrt{63})} + 8 - \sqrt{63}\)

= 8 + 2 + 8

= 18

Answer = D
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Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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New post 12 Jan 2015, 08:37
PareshGmat wrote:
Easy method:

\((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2\)

Multiply \(\frac{1}{\sqrt{8 - \sqrt{63}}} * \frac{\sqrt{8 + \sqrt{63}}}{\sqrt{8 + \sqrt{63}}} = \sqrt{8 + \sqrt{63}}\)

similarly\(\frac{1}{\sqrt{8 +\sqrt{63}}} * \frac{\sqrt{8 - \sqrt{63}}}{\sqrt{8 - \sqrt{63}}} = \sqrt{8 - \sqrt{63}}\)

\(= (\sqrt{8 + \sqrt{63}} + \sqrt{8 -\sqrt{63}})^2\)

\(= 8 + \sqrt{63} + 2 * \sqrt{(8 + \sqrt{63})(8 - \sqrt{63})} + 8 - \sqrt{63}\)

= 8 + 2 + 8

= 18

Answer = D


Thnx Paresh the method is most useful
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Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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New post 13 Jan 2019, 02:14
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Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 = &nbs [#permalink] 13 Jan 2019, 02:14
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