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Sub 505 (Easy)|   Algebra|      
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registerincog
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If x is positive, then 1/(root(x+1) + root(x)) = 21 Nov 2013, 02:03
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D
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5% (low)

Question Stats:

83% (00:59) correct 18% (01:48) wrong based on 240 sessions

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If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1

B) x

C) \(\frac{1}{x}\)

D) \(\sqrt{x+1}-\sqrt{x}\)

E) \(\sqrt{x+1}+\sqrt{x}\)
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D
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Bunuel
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If x is positive, then 1/(root(x+1) + root(x)) = 21 Nov 2013, 02:11
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registerincog
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)
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Rationalize the fraction by multiplying it by \(\frac{\sqrt{x+1}-\sqrt{x}}{\sqrt{x+1}-\sqrt{x}}\) and apply \((a+b)(a-b)=a^2-b^2\) to the denominator:

\(\frac{1}{\sqrt{x+1}+\sqrt{x}}*\frac{\sqrt{x+1}-\sqrt{x}}{\sqrt{x+1}-\sqrt{x}}=\frac{\sqrt{x+1}-\sqrt{x}}{x+1-x}=\sqrt{x+1}-\sqrt{x}\).

Answer: D.
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If x is positive, then 1/(root(x+1) + root(x)) = 18 Dec 2013, 05:42
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Am I being stupid, or is the question missing something?

I.e. should there not be a question mark or something at the end, or at least an equal sign.
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If x is positive, then 1/(root(x+1) + root(x)) = 18 Dec 2013, 06:53
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wuhanmatt
Am I being stupid, or is the question missing something?

I.e. should there not be a question mark or something at the end, or at least an equal sign.
Show more

You are right there should be an equal sign at the end. Edited. Thank you.
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If x is positive, then 1/(root(x+1) + root(x)) = 11 Sep 2014, 03:01
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registerincog
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)
Show more

For such type of questions, change the middle sign & reciprocal

For example, \(\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}\)

Answer = D
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If x is positive, then 1/(root(x+1) + root(x)) = 27 Jul 2018, 12:25
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PareshGmat
registerincog
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)

For such type of questions, change the middle sign & reciprocal

For example, \(\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}\)

Answer = D
Show more

I just encountered this question as part of my daily questions from the log and only got it right by guessing.

Could you elaborate how you get root 5&6?

Thanks and best regards,
Chris
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If x is positive, then 1/(root(x+1) + root(x)) = 28 Jul 2018, 04:34
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Arro44
PareshGmat
registerincog
If x is positive, then \(\frac{1}{\sqrt{x+1}+\sqrt{x}}=\)

A) 1
B) x
C) \(\frac{1}{x}\)
D) \(\sqrt{x+1}-\sqrt{x}\)
E) \(\sqrt{x+1}+\sqrt{x}\)

For such type of questions, change the middle sign & reciprocal

For example, \(\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}\)

Answer = D

I just encountered this question as part of my daily questions from the log and only got it right by guessing.

Could you elaborate how you get root 5&6?

Thanks and best regards,
Chris
Show more

This is explained HERE.

This algebraic manipulation is called rationalization and is performed to eliminate irrational expression in the denominator.

Questions involving rationalization to practice:
https://gmatclub.com/forum/in-the-given ... 59791.html
https://gmatclub.com/forum/if-x-0-then-106291.html
https://gmatclub.com/forum/if-n-is-posit ... 31236.html
https://gmatclub.com/forum/consider-a-qu ... 31083.html
https://gmatclub.com/forum/in-the-diagra ... 39282.html
https://gmatclub.com/forum/in-the-diagra ... 29962.html
https://gmatclub.com/forum/the-perimeter ... 27049.html
https://gmatclub.com/forum/which-of-the- ... 98531.html
https://gmatclub.com/forum/if-x-is-posit ... 63491.html
https://gmatclub.com/forum/1-2-sqrt3-64378.html
https://gmatclub.com/forum/if-a-square-m ... 99359.html

Hope it helps.
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If x is positive, then 1/(root(x+1) + root(x)) = 01 Oct 2023, 12:23
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