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If x is positive, then 1/(root(x+1) + root(x)) =

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If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 21 Nov 2013, 02:03
2
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

83% (00:58) correct 17% (01:58) wrong based on 162 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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Re: If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 21 Nov 2013, 02:11
2
registerincog wrote:
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) \(\sqrt{x+1}+\sqrt{x}\)


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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Re: If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 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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Re: If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 18 Dec 2013, 06:53
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Re: If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 11 Sep 2014, 03:01
3
registerincog wrote:
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
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Re: If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 27 Jul 2018, 12:25
PareshGmat wrote:
registerincog wrote:
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
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Re: If x is positive, then 1/(root(x+1) + root(x)) =  [#permalink]

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New post 28 Jul 2018, 04:34
1
Arro44 wrote:
PareshGmat wrote:
registerincog wrote:
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


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

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: If x is positive, then 1/(root(x+1) + root(x)) = &nbs [#permalink] 28 Jul 2018, 04:34
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