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# If n is positive, which of the following is equal to

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Intern
Joined: 05 Nov 2008
Posts: 6
If n is positive, which of the following is equal to [#permalink]

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05 Nov 2008, 21:26
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Question Stats:

81% (01:25) correct 19% (01:11) wrong based on 135 sessions

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If n is positive, which of the following is equal to $$\frac{1}{\sqrt{n+1}-\sqrt{n}}$$

A. 1

B. $$\sqrt{2n+1}$$

C. $$\frac{\sqrt{n+1}}{\sqrt{n}}$$

D. $$\sqrt{n+1}-\sqrt{n}$$

E. $$\sqrt{n+1}+\sqrt{n}$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-positive-which-of-the-following-is-equal-to-31236.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Jul 2013, 10:39, edited 1 time in total.
Edited the question, added the OA and moved to PS forum.
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Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12

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05 Nov 2008, 22:01
just multiple numerator and denominator with sqrt(n+1)+sqrt(n)

E it is..
Manager
Joined: 14 Jun 2007
Posts: 168
Location: Vienna, Austria

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06 Nov 2008, 00:33
freshina
cant that be smiplified to and hence be answer A ?

cheers
Director
Joined: 14 Aug 2007
Posts: 727

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06 Nov 2008, 06:35
fresinha12 wrote:
just multiple numerator and denominator with sqrt(n+1)+sqrt(n)

E it is..

agree with E, same approach
Intern
Joined: 17 Dec 2012
Posts: 7
Concentration: Entrepreneurship, Finance
GMAT Date: 12-13-2013
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31 Jul 2013, 10:31
domleon wrote:
freshina
cant that be smiplified to and hence be answer A ?

cheers

A also works for me.

Why E?
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Joined: 02 Sep 2009
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31 Jul 2013, 10:40
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Abakup wrote:
domleon wrote:
freshina
cant that be smiplified to and hence be answer A ?

cheers

A also works for me.

Why E?

If n is positive, which of the following is equal to $$\frac{1}{\sqrt{n+1}-\sqrt{n}}$$

A. 1

B. $$\sqrt{2n+1}$$

C. $$\frac{\sqrt{n+1}}{\sqrt{n}}$$

D. $$\sqrt{n+1}-\sqrt{n}$$

E. $$\sqrt{n+1}+\sqrt{n}$$

This question is dealing with rationalisation of a fraction. Rationalisation is performed to eliminate irrational expression in the denominator. For this particular case we can do this by applying the following rule: $$(a-b)(a+b)=a^2-b^2$$.

Multiple both numerator and denominator by $$\sqrt{n+1}+\sqrt{n}$$: $$\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}-\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2-(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1-n}=\sqrt{n+1}+\sqrt{n}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-positive-which-of-the-following-is-equal-to-31236.html
_________________
Re: question--30   [#permalink] 31 Jul 2013, 10:40
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