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1. If $\sqrt{3}$ = 1.732 is given, then the value of $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ is = ?

A. 11.732

B. 13.928

C. 12.928

D. 13.925

Solution:

\begin{aligned} \sqrt{3} = 1.732 \\ \Rightarrow \frac{2 + \sqrt{3}}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} \\ \Rightarrow \frac{{(2 + \sqrt{3})}^{2}}{4 - 3} \\ \Rightarrow 4 + 3 + 4 \sqrt{3} \\ \Rightarrow 7 + 4 \times 1.732 \\ \Rightarrow 7 + 6.928 \\ \Rightarrow 13.928 \end{aligned}

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