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1. Given $\sqrt{2}$ = 1.414, the value of $\sqrt{8}$ $+$ $2 \sqrt{32}$ $-$ $3 \sqrt{128}$ $+$ $4 \sqrt{50}$ is = ?

A. 8.484

B. 8.526

C. 8.426

D. 8.876

Solution:

\begin{aligned} \sqrt{2} = 1.414 \\ \Rightarrow \sqrt{8} + 2 \sqrt{32} - 3 \sqrt{128} + 4 \sqrt{50} \\ \Rightarrow 2 \sqrt{2} + 2 \times 4 \sqrt{2} - 3 \times 8 \sqrt{2} + 4 \times 5 \sqrt{2} \\ \Rightarrow 2 \sqrt{2} + 8 \sqrt{2} - 24 \sqrt{2} + 20 \sqrt{2} \\ \Rightarrow 6 \sqrt{2} \\ \Rightarrow 6 \times 1.414 \\ \Rightarrow 8.484 \end{aligned}

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