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

The correct option is C

0.4142

$\sqrt{2}=1.4142,$

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

(Rationalising the denominator)

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

$=\sqrt{\frac{(\sqrt{2}-1{)}^2}{1}}=\sqrt{2}-1-1.4142-1$

$0.4142$