Question

If $\sqrt{2}=1.414$, then the value of $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is :

• A. 0.207
• B. 2.414
• C. 0.621
• D. 0.414

Answer 1

The correct option is D 0.414

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

$\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}=\sqrt{2}-1=1.414-1=0.414$