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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 , given: 397

Which expression is equivalent to ? [#permalink]
Expert's post 00:00

Question Stats: 57% (00:40) correct 42% (00:18) wrong based on 7 sessions
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. $$7-4\sqrt{3}$$
[Reveal] Spoiler: OA

_________________

Sandy
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Joined: 01 Nov 2017
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Kudos [?]: 111 , given: 4

Re: Which expression is equivalent to ? [#permalink]
Expert's post
sandy 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. $$7-4\sqrt{3}$$

Hi...

You can do this in two ways...

(I) Algebraic ..
Since the denominator has a square root, use $$(a-b)(a+b)=a^2-b^2$$ to remove it..
$$\frac{2 - \sqrt{3}}{2 + \sqrt{3}}=\frac{(2 - \sqrt{3})^2}{(2 + \sqrt{3})(2 - \sqrt{3})}=\frac{4+3 -4 \sqrt{3})^2}{(2)^2-(\sqrt{3})^2}=7-4\sqrt{3}$$

E

(II) Or simply use calculator to find the answer..
$$\frac{2 - \sqrt{3}}{2 + \sqrt{3}}$$ has to be positive as $$2>\sqrt{3}$$..value = 0.072
A, B and D are negative
C would be more.. = 0.84

only E left .. $$7-4\sqrt{3}=7-6.93=0.07$$
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: Which expression is equivalent to ?   [#permalink] 11 Jan 2019, 06:11
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