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 .. \(7-4\sqrt{3}=7-6.93=0.07\)