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1. Evaluate: $16 \sqrt{\frac{3}{4}} - 9 \sqrt{\frac{4}{3}}$ if $\sqrt{12}$ = 3.46

A. 3.46

B. 10.38

C. 13.84

D. 24.22

Solution:

\begin{aligned} 16 \sqrt{\frac{3}{4}} - 9 \sqrt{\frac{4}{3}} \\ \Rightarrow 16 \sqrt{\frac{3 \times 4}{4 \times 4}} - 9 \sqrt{\frac{3 \times 4}{3 \times 3}} \\ \Rightarrow 16 \times \frac{\sqrt{12}}{4} - \frac{9 \sqrt{12}}{3} \\ \Rightarrow 4 \sqrt{12} - 3 \sqrt{12} \\ \Rightarrow \sqrt{12} \\ \Rightarrow 3.46 \end{aligned}

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