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

The correct option is D. $0.4142$

Given: $\sqrt{2}=1.4142,$

Now, rationalizing the given expression we get,

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

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

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

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

$=\sqrt{2}-1$

$=1.4142-1$

$=0.4142$

Hence, $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}=0.4142$