MCQ
Write the correct answer in the following:
If $\sqrt{2}=1.4142,$ then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to
If $\sqrt{2}=1.4142,$ then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to
- A2.4142
- B5.8282
- C0.4142
- D0.1718
✓
Answer
- 0.4142
Solution:
$\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}=\sqrt{\frac{\sqrt{2}-1}{{\sqrt{2}+1}}\cdot\frac{\sqrt{2}-1}{\sqrt{2}-1}}$
$[$Inside the root, multiplying numerator and denominator by $(\sqrt{2}-1)]$
$=\sqrt{\frac{(\sqrt{2}-1)^2}{(\sqrt{2})^2-(1)^2}}$ $ [\text{using identity (a}-\text{b})(\text{a+b})=\text{a}^2-\text{b}^2]$
$=\sqrt{\frac{(\sqrt{2}-1)^2}{2-1}}=\sqrt{2}-1=(1.4142...)-1=0.4142...$
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