If 2 = 1.414 , the square root of 2 - 1 2 + 1 is nearest to = ?

Answer: Option B

$$\begin{array}{rl}& =\frac{\sqrt{2}-1}{\sqrt{2}+1}\\ & =\frac{\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)}\times \frac{\left(\sqrt{2}-1\right)}{\left(\sqrt{2}-1\right)}\\ & ={\left(\sqrt{2}-1\right)}^2\\ & \therefore \sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}\\ & =\left(\sqrt{2}-1\right)\\ & =\left(1.414-1\right)\\ & =0.414\end{array}$$