MCQ
An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is:
- A$\big(\sqrt{2}+\sqrt{3}\big)$
- B$\big(\sqrt{2}\times\sqrt{3}\big)$
- C$5^{\frac{1}{4}}$
- ✓$6^{\frac{1}{4}}$
✓
Answer
Correct option: D.
$6^{\frac{1}{4}}$
An irrational number between $a$ and $b$ is given by $\sqrt{\text{ab}}$
An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is
$\sqrt{\sqrt{2}+\sqrt{3}}=\big(\sqrt{6}\big)^{\frac{1}{2}}$
$=6^{\frac{1}{2}\times\frac{1}{2}}$
$=6^{\frac{1}{4}}$
Hence, the correct answer is option $(d).$
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