# Find the value

Question:

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

(a) $0.207$

(b) $2.414$

(c) $0.414$

(d) $0.621$

Solution:

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

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

$=\sqrt{3-2 \sqrt{2}}$

$=\sqrt{3-2 \times 1.414}$

$=\sqrt{3-2.828}$

$=\sqrt{0.172}$

$=0.414$

Hence, the correct answer is option (c).