Question

If $\sqrt{2}=1.414\mathrm{then}\sqrt{\frac{\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)}}=?$
(a) 0.207
(b) 2.414
(c) 0.414
(d) 0.621

Answer 1

$$\begin{gathered} \sqrt{\frac{\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)}}=\sqrt{\frac{\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)}\times \frac{\left(\sqrt{2}-1\right)}{\left(\sqrt{2}-1\right)}}=\sqrt{\frac{{\left(\sqrt{2}-1\right)}^2}{2-1}} \\ =\sqrt{\frac{2+1-2\sqrt{2}}{1}} \\ =\sqrt{3-2\sqrt{2}} \\ =\sqrt{3-2\times 1.414} \\ =\sqrt{3-2.828} \\ =\sqrt{0.172} \\ =0.414 \end{gathered}$$
Hence, the correct answer is option (c).