Question

If $\sqrt{2}=1.4142$... then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to

A) $2.4142$
B) $5.8282$
C) $0.4142$
D) $0.1718$

Answer 1

Option C) is correct.

Given:$\sqrt{2}=1.4142$

On rationalizing, we get,

$\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}=\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}\times \frac{\sqrt{2}-1}{\sqrt{2}-1}}$ [Multiplying numerator and denominator by $(\sqrt{2}-1)$]

$=\sqrt{\frac{(\sqrt{2}-1{)}^2}{(\sqrt{2}{)}^2-(1{)}^2}}$

$=\sqrt{\frac{(\sqrt{2}-1{)}^2}{2-1}}=\sqrt{2}-1=\left(\mathrm{1.4142...}\right)-1=0.4142$