Question

If $\sqrt{2}=1.414,then\sqrt{\frac{\sqrt{2}-1}{(\sqrt{2}+1)}}=$?

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

Answer 1

The correct option is A

0.414

$\sqrt{\frac{\sqrt{2}-1}{(\sqrt{2}+1)}}=\frac{\sqrt{2}-1}{(\sqrt{2}+1)}\times \frac{\sqrt{2}-1}{(\sqrt{2}-1)}=\frac{(\sqrt{2}-1)}{(2-1)}=(\sqrt{2}-1{)}^2\therefore \sqrt{\frac{(\sqrt{2}-1)}{\sqrt{2}+1}}=\sqrt{(\sqrt{2}-1{)}^2}=(\sqrt{2}-1)=(1.414-1)=0.414$