Question

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

(a) 0.1718

(b) 5.8282

(c) 0.4142

(d) 2.4142

Answer 1

Given that , we need to find the value of .

We can rationalize the denominator of the given expression. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

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

Putting the value of , we get

Hence the value of the given expression is 0.14142 and correct choice is.