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

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SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1793
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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31 Dec 2014, 00:10
2
1
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:09) correct 28% (02:29) wrong based on 74 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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Joined: 22 Oct 2014
Posts: 88
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45
GPA: 3.8
WE: General Management (Consulting)
The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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31 Dec 2014, 02:04
1
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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SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1793
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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31 Dec 2014, 03:52
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

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Joined: 12 Jun 2014
Posts: 3
Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =  [#permalink]

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12 Jan 2015, 09:37
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

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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13 Jan 2019, 03:14
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Re: The expression (1/\sqrt{8 - \sqrt{63}} +1/\sqrt{8 +\sqrt{63}})^2 =   [#permalink] 13 Jan 2019, 03:14
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