MCQ
If $\sqrt{2}=1.414$ than $\sqrt{\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}}=?$
- A0.207
- B0.414
- C2.414
- D0.621
✓
Answer
- 0.414
Solution:
$\sqrt{\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}}$
$=\sqrt{\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}\times\frac{(\sqrt{2}-1)}{(\sqrt{2}-1)}}$
$=\sqrt{\frac{(\sqrt{2}-1)^2}{(\sqrt{2})^2-(1)^2}}$
$=\sqrt{\frac{(\sqrt{2}-1)^2}{2-1}}$
$=\sqrt{(\sqrt{2}-1)^2}$
$=1.414-1$
$=0.414$
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