MCQ
If $\sqrt{2}=1.414$, then the value of $\frac{1}{1+\sqrt{2}}$ is
- A$1 / 2$
- B$2.414$
- C-0.414
- ✓0.414
✓
Answer
Correct option: D.
0.414
(d)
A rationalising factor of $1+\sqrt{2}$ is $1-\sqrt{2}$.
$\therefore$ $ \frac{1}{1+\sqrt{2}}=\frac{1-\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}=\frac{1-\sqrt{2}}{1-2}=\sqrt{2}-1=1.414-1=0.414 $
A rationalising factor of $1+\sqrt{2}$ is $1-\sqrt{2}$.
$\therefore$ $ \frac{1}{1+\sqrt{2}}=\frac{1-\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}=\frac{1-\sqrt{2}}{1-2}=\sqrt{2}-1=1.414-1=0.414 $
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