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Which expression is equivalent to ?
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27 Oct 2018, 16:51
27 Oct 2018, 16:51
Expert Reply
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Question Stats:
57% (00:45) correct
42% (01:49) wrong based on 19 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. \(7-4\sqrt{3}\)
A. \(\frac{-1}{5}\)
B. \(-1\)
C. \(\frac{4\sqrt{3}-1}{7}\)
D. \(4\sqrt{3}-7\)
E. \(7-4\sqrt{3}\)
Re: Which expression is equivalent to ?
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11 Jan 2019, 06:11
11 Jan 2019, 06:11
Expert Reply
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. \(7-4\sqrt{3}\)
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 .. \(7-4\sqrt{3}=7-6.93=0.07\)
gmatclubot
Re: Which expression is equivalent to ? [#permalink]
11 Jan 2019, 06:11
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