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

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

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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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Re: question--30 [#permalink]

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

E it is..

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Re: question--30 [#permalink]

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

cheers

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Re: question--30 [#permalink]

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New post 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

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Re: question--30 [#permalink]

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New post 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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Re: question--30 [#permalink]

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New post 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 \(\sqrt{n+1}+\sqrt{n}\): \(\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1}-\sqrt{n})(\sqrt{n+1}+\sqrt{n})}=\frac{\sqrt{n+1}+\sqrt{n}}{(\sqrt{n+1})^2-(\sqrt{n})^2)}=\frac{\sqrt{n+1}+\sqrt{n}}{n+1-n}=\sqrt{n+1}+\sqrt{n}\).

Answer: E.

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