Question

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

• A. 2.4142
• B. 5.8282
• C. 0.4142
• D. 0.1718

Answer 1

The correct option is C 0.4142

$\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$$=\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}.\frac{\sqrt{2}-1}{\sqrt{2}-1}}$
[inside the root, mulitplying the numerator and denominator by $(\sqrt{2}-1)$
[Using identity $(a-b)(a+b)=a^2-b^2$]
$=\sqrt{\frac{(\sqrt{2}-1{)}^2}{(\sqrt{2}{)}^2-(1{)}^2}}=\sqrt{\frac{(\sqrt{2}-1{)}^2}{2-1}}=\sqrt{2}-1=\left(\mathrm{1.4142....}\right)-1=0.4142$