An irrational number between 2 and 3 is: - Vidyadip

Question

An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is:

✓

Answer

$6^{\frac{1}{4}}$
Solution:
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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