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(2+√7)=?

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Senior Manager
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(2+√7)=?  [#permalink]

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New post 29 Jun 2014, 13:00
4
10
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:25) correct 29% (01:48) wrong based on 238 sessions

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(2+√7)=?

A) 3/5
B) √3/(√7+2)
C) 3/(√7+2)
D) √3/(√7−2)
E) 3/(√7 − 2)
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Re: (2+√7)=?  [#permalink]

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New post 29 Jun 2014, 13:07
1
2
goodyear2013 wrote:
(2+√7)=?

A) 3/5
B) √3/(√7+2)
C) 3/(√7+2)
D) √3/(√7−2)
E) 3/(√7 − 2)


multiply numerator and denominator with √7-2, we will get

= (√7+2)(√7-2)/(√7-2)
=(√7)^2-(2)^2/ √7-2
=7-4/(√7-2)
=3/(√7-2)

hence E
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Re: (2+√7)=?  [#permalink]

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New post 29 Jun 2014, 13:09
3
goodyear2013 wrote:
(2+√7)=?

A) 3/5
B) √3/(√7+2)
C) 3/(√7+2)
D) √3/(√7−2)
E) 3/(√7 − 2)


Multiply by \(\frac{2-\sqrt{7}}{2-\sqrt{7}}\):

\(2+\sqrt{7}*\frac{2-\sqrt{7}}{2-\sqrt{7}}=\frac{4-7}{2-\sqrt{7}}=\frac{-3}{2-\sqrt{7}}=\frac{3}{\sqrt{7}-2}\).

Answer: E.

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Hope it helps.
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Re: (2+√7)=?  [#permalink]

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New post 08 Aug 2017, 20:07
1
We know that (2+√7)=(√7 + 2)

In order to find the value of the expression,
we multiply and divide by the same number.
\(\frac{(√7 + 2)((√7 - 2)}{(√7 - 2)}\)
Simplifying the numerator we get (√7)^2 - (2)^2 = 7 - 4 = 3

Therefore, the value of the expression is \(\frac{3}{(√7 - 2)}\) (Option E)
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Re: (2+√7)=?  [#permalink]

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New post 29 Sep 2017, 02:03
I find it hard to grasp why a GMAT question would have a radical in the denominator for answers......? I believe from all the resources I have encountered with, there should not be a radical in the answer.........
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(2+√7)=?  [#permalink]

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New post 27 Apr 2019, 17:52
Can someone explain why you wouldn't just square \((2+\sqrt{7})\)? That was my immediate approach rather than using the conjugate which I thought is mainly used when you have a root in the denominator of the question, which is not the case here.
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(2+√7)=?   [#permalink] 27 Apr 2019, 17:52
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