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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] New post 26 Oct 2007, 05:08
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If n is positive, which of the following is equal to 1/{sqrt(n+1) - sqrt(n}?

A. 1
B. sqrt(2n+1)
C. sqrt(n+1) / sqrt(n)
D. sqrt(n+1) - sqrt(n)
E. sqrt(n+1) + sqrt(n)


Answer: E (highlight to see)
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Re: PS - Roots [#permalink] New post 26 Oct 2007, 05:28
mistahfold wrote:
If n is positive, which of the following is equal to 1/{sqrt(n+1) - sqrt(n}?

A. 1
B. sqrt(2n+1)
C. sqrt(n+1) / sqrt(n)
D. sqrt(n+1) - sqrt(n)
E. sqrt(n+1) + sqrt(n)


Answer: E (highlight to see)


E.

1/[sqrt(n+1) - sqrt(n)] = 1/[sqrt(n+1) - sqrt(n)] * [sqrt(n+1) + sqrt(n)]/[sqrt(n+1) + sqrt(n)]

= sqrt(n+1) + sqrt(n)
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 [#permalink] New post 26 Oct 2007, 07:48
young_gun wrote:
can someone elaborate on this one? thx


1/[sqrt(n+1) - sqrt(n)]
= [sqrt(n+1) + sqrt(n)]/[sqrt(n+1) + sqrt(n)] * 1/[sqrt(n+1) - sqrt(n)]
= [sqrt(n+1) + sqrt(n)] / [ (sqrt(n+1) + sqrt(n)) * (sqrt(n+1) - sqrt(n)) ]
= [sqrt(n+1) + sqrt(n)] / [ (sqrt(n+1)) ^2 - (sqrt(n)) ^2 ]
= [sqrt(n+1) + sqrt(n)] / [ (n+1) - n ]
= sqrt(n+1) + sqrt(n)

:)

Edit 2 : young_gun.... U have deleted faster than replied... well :) :wink:
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 [#permalink] New post 26 Oct 2007, 07:56
Fig wrote:
young_gun wrote:
can someone elaborate on this one? thx


1/[sqrt(n+1) - sqrt(n)]
= [sqrt(n+1) + sqrt(n)]/[sqrt(n+1) + sqrt(n)] * 1/[sqrt(n+1) - sqrt(n)]
= [sqrt(n+1) + sqrt(n)] / [ (sqrt(n+1) + sqrt(n)) * (sqrt(n+1) - sqrt(n)) ]
= [sqrt(n+1) + sqrt(n)] / [ (sqrt(n+1)) ^2 - (sqrt(n)) ^2 ]
= [sqrt(n+1) + sqrt(n)] / [ (n+1) - n ]
= sqrt(n+1) + sqrt(n)

:)

Edit 2 : young_gun.... U have deleted faster than replied... well :) :wink:


I realized we could just multiply by (a+b)/(a+b)...I keep forgetting this trick. Thanks for the reply though!
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Re: PS - Roots [#permalink] New post 26 Oct 2007, 08:58
i get E...

1/[sqrt(n+1)-sqrt(n)] * [sqrt(n+1)+sqrt(n)]/[sqrt(n+1)+sqrt(n)]

you get

[sqrt(n+1)+sqrt(n)]/[(n+1)-n]

the denominator n cancels..

mistahfold wrote:
If n is positive, which of the following is equal to 1/{sqrt(n+1) - sqrt(n}?

A. 1
B. sqrt(2n+1)
C. sqrt(n+1) / sqrt(n)
D. sqrt(n+1) - sqrt(n)
E. sqrt(n+1) + sqrt(n)


Answer: E (highlight to see)
Re: PS - Roots   [#permalink] 26 Oct 2007, 08:58
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