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1/(2 - \sqrt3) = ?

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1/(2 - \sqrt3) = ? [#permalink]

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New post 23 May 2008, 11:00
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:40) correct 23% (01:04) wrong based on 98 sessions

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\(\frac{1}{2 - \sqrt{3}} = ?\)

A. \(\sqrt{3} - 2\)
B. \(2 + \sqrt{3}\)
C. \(\sqrt{2} + \sqrt{3}\)
D. \(2 - \sqrt{3}\)
E. \(\sqrt{3} + 4\)
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 May 2015, 10:02, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: 1/(2 - \sqrt3) = ? [#permalink]

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New post 23 May 2008, 11:04
i get B

just multiply the equation by [2+sqrt(3)] / [2+sqrt(3)]
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Re: 1/(2 - \sqrt3) = ? [#permalink]

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New post 26 May 2015, 07:14
OMG IT"S VERY HARD!!!! :shock: :shock: :shock: :shock: :shock:
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Re: 1/(2 - \sqrt3) = ? [#permalink]

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New post 26 May 2015, 09:51
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Hi Sandra2U,

The GMAT will often test you on ideas/concepts that you know, but in ways that you're not used to thinking about.

This question is built on 2 concepts:
1) Re-writing fractions
2) Quadratics (and how to "get rid of" radicals)

When re-writing a fraction, we're allowed to MULTIPLY or DIVIDE both parts of a fraction (as long as we do it to both parts).

For example...

2/4 = 1/2

1/3 = 5/15

With Quadratics, there are 3 that you should have memorized for Test Day. Here, we're dealing with this one....

(X-Y)(X+Y) = X^2 - Y^2

So, if the first parenthesis is (2−√3), the second parenthesis should be (2+√3).

From here, the math is just as chengliu describes.

As you continue to practice, get in the habit of thinking about what the question REMINDS you of - chances are that those exact concepts/rules are what you're supposed to use to answer the question.

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Re: 1/(2 - \sqrt3) = ? [#permalink]

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New post 26 May 2015, 10:02
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chengliu wrote:
\(\frac{1}{2 - \sqrt{3}} = ?\)

A. \(\sqrt{3} - 2\)
B. \(2 + \sqrt{3}\)
C. \(\sqrt{2} + \sqrt{3}\)
D. \(2 - \sqrt{3}\)
E. \(\sqrt{3} + 4\)


Multiply both numerator and denominator by \((2 + \sqrt{3})\). That yields \(\frac{2 + \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} = \frac{2 + \sqrt{3}}{4 - 3} = 2 + \sqrt{3}\).


Answer: B.

This algebraic manipulation is called rationalisation and is performed to eliminate irrational expression in the denominator. For this particular case we are doing rationalisation by applying the following rule: \((a-b)(a+b)=a^2-b^2\). The concept of rationalisation of a fraction used to solve this problem is often tested on the GMAT.

Questions relied on this technique:
if-x-0-then-106291.html
if-n-is-positive-which-of-the-following-is-equal-to-31236.html
consider-a-quarter-of-a-circle-of-radius-16-let-r-be-the-131083.html
in-the-diagram-not-drawn-to-scale-sector-pq-is-a-quarter-139282.html
in-the-diagram-what-is-the-value-of-x-129962.html
the-perimeter-of-a-right-isoscles-triangle-is-127049.html
which-of-the-following-is-equal-to-98531.html
if-x-is-positive-then-1-root-x-1-root-x-163491.html

Hope it helps.
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Re: 1/(2 - \sqrt3) = ?   [#permalink] 26 May 2015, 10:02
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