Problem: Simplify (276−634)2\left(\sqrt[6]{27}-\sqrt{6 \dfrac{3}{4}}\right)^{2}(627−643)2.
Answer Choices:
A. 34\dfrac{3}{4}43
B. 32\dfrac{\sqrt{3}}{2}23
C. 334\dfrac{3 \sqrt{3}}{4}433
D. 32\dfrac{3}{2}23
E. 332\dfrac{3 \sqrt{3}}{2}233
Solution:
(276−634)2=[(33)1/6−(274)1/2]2=[3−332]2=[−32]2=34\begin{aligned} \left(\sqrt[6]{27}-\sqrt{6 \dfrac{3}{4}}\right)^{2}= & {\left[\left(3^{3}\right)^{1 / 6}-\left(\dfrac{27}{4}\right)^{1 / 2}\right]^{2}=\left[\sqrt{3}-\dfrac{3 \sqrt{3}}{2}\right]^{2} } \\ & =\left[\dfrac{-\sqrt{3}}{2}\right]^{2}=\dfrac{3}{4} \end{aligned} (627−643)2=[(33)1/6−(427)1/2]2=[3−233]2=[2−3]2=43