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# (2+√7)=?

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Senior Manager
Joined: 21 Oct 2013
Posts: 411

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29 Jun 2014, 13:00
4
10
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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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Joined: 13 Jun 2013
Posts: 266

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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
Math Expert
Joined: 02 Sep 2009
Posts: 58427

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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 $$\frac{2-\sqrt{7}}{2-\sqrt{7}}$$:

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

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Hope it helps.
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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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Status: Studying for GMAT
Joined: 06 Jan 2015
Posts: 19
Location: United Kingdom

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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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Joined: 31 Aug 2014
Posts: 11

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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.
(2+√7)=?   [#permalink] 27 Apr 2019, 17:52
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