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# Which expression is equivalent to (2 - 3^(1/2))/(2 + 3^(1/2))

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Math Expert
Joined: 02 Sep 2009
Posts: 58344
Which expression is equivalent to (2 - 3^(1/2))/(2 + 3^(1/2))  [#permalink]

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28 Oct 2018, 23:40
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Difficulty:

15% (low)

Question Stats:

83% (01:21) correct 18% (01:54) wrong based on 44 sessions

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Which expression is equivalent to $$\frac{2 - \sqrt{3}}{2 + \sqrt{3}}$$?

A. $$\frac{-1}{5}$$

B. $$-1$$

C. $$\frac{4\sqrt{3}-1}{7}$$

D. $$4\sqrt{3}-7$$

E. $$7-4\sqrt{3}$$

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Re: Which expression is equivalent to (2 - 3^(1/2))/(2 + 3^(1/2))  [#permalink]

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28 Oct 2018, 23:45
Multiply numerator and denominator by 2- 3^1/2 and solve the question.

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Re: Which expression is equivalent to (2 - 3^(1/2))/(2 + 3^(1/2))  [#permalink]

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28 Oct 2018, 23:46
Bunuel wrote:
Which expression is equivalent to $$\frac{2 - \sqrt{3}}{2 + \sqrt{3}}$$?

A. $$\frac{-1}{5}$$

B. $$-1$$

C. $$\frac{4\sqrt{3}-1}{7}$$

D. $$4\sqrt{3}-7$$

E. $$7-4\sqrt{3}$$

Rationalise $$\frac{2 - \sqrt{3}}{2 + \sqrt{3}}$$

$$\frac{2 - \sqrt{3}}{2 + \sqrt{3}}$$ * $$\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$$

==> $$(2 - \sqrt{3})^2$$ =>$$7-4\sqrt{3}$$

Hence E
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Resource: GMATPrep RCs With Solution
Re: Which expression is equivalent to (2 - 3^(1/2))/(2 + 3^(1/2))   [#permalink] 28 Oct 2018, 23:46
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