Problem: The expression 43−34\sqrt{\dfrac{4}{3}}-\sqrt{\dfrac{3}{4}}34−43 is equal to:
Answer Choices:
A. 3/6\sqrt{3} / 63/6
B. −3/6-\sqrt{3} / 6−3/6
C. −3/6\sqrt{-3} / 6−3/6
D. 53/65 \sqrt{3} / 653/6
E. 111 Solution:
43−34=233−32=43−336=36\sqrt{\dfrac{4}{3}}-\sqrt{\dfrac{3}{4}}=\dfrac{2 \sqrt{3}}{3}-\dfrac{\sqrt{3}}{2}=\dfrac{4 \sqrt{3}-3 \sqrt{3}}{6}=\dfrac{\sqrt{3}}{6}34−43=323−23=643−33=63 \quad