MCQ
An irrational number between $\frac{1}{7}$ and $\frac{2}{7}$ is
- A$\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$
- B$\frac{1}{7} \times \frac{2}{7}$
- ✓$\sqrt{\frac{1}{7} \times \frac{2}{7}}$
- Dnone of these
✓
Answer
Correct option: C.
$\sqrt{\frac{1}{7} \times \frac{2}{7}}$
(c)
We know that $\frac{a+b}{2}$ and $\sqrt{a b}$ are real numbers between any two real numbers. So $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$ and $\sqrt{\frac{1}{7} \times \frac{2}{7}}$ are real numbers between 1/7 and 2/7.
We observe that $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$ and $\frac{1}{7} \times \frac{2}{7}$ are rational numbers.
So, options (a) and (b) are incorrect. Clearly $\sqrt{\frac{1}{7} \times \frac{2}{7}}=\frac{\sqrt{2}}{7}$ is an irrational number between 1/7 and 2/7 So, option (c) is is correct.
We know that $\frac{a+b}{2}$ and $\sqrt{a b}$ are real numbers between any two real numbers. So $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$ and $\sqrt{\frac{1}{7} \times \frac{2}{7}}$ are real numbers between 1/7 and 2/7.
We observe that $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$ and $\frac{1}{7} \times \frac{2}{7}$ are rational numbers.
So, options (a) and (b) are incorrect. Clearly $\sqrt{\frac{1}{7} \times \frac{2}{7}}=\frac{\sqrt{2}}{7}$ is an irrational number between 1/7 and 2/7 So, option (c) is is correct.
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