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).
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