Question

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

(a)$(\sqrt{2}+\sqrt{3})$

(b)$\sqrt{2}\times \sqrt{3}$

(c)$5^{\frac{1}{4}}$

(d)$6^{\frac{1}{4}}$

Answer 1

An irrational number between $\sqrt{2}and\sqrt{3}$ is $\sqrt{\sqrt{2}\times \sqrt{3}}=\sqrt{\sqrt{6}}=\left(\right(6{)}^{\frac{1}{2}}{)}^{\frac{1}{2}}=6^{\frac{1}{4}}$

(d)$6^{\frac{1}{4}}$