Question

The two irrational nos.between root two and root three are

root two,Fourth root of six

fourth root of three,sixth root of 3

eighth root of 6,fourth root of 3

Answer 1

The irrational number lying between two irrational numbers a and b is give by $\sqrt{ab}$
so, an irrational number between $\sqrt{2}and\sqrt{3}$ is given by $\sqrt{\sqrt{2}\times \sqrt{3}}=\sqrt{\sqrt{2\times 3}}=\sqrt{\sqrt{6}}=\sqrt[4]{6}=\mathrm{fourth}\mathrm{root}\mathrm{of}6$

another irrational number is $\sqrt{\sqrt{3}\times 6^{1/4}}=\sqrt{3^{1/2}\times 6^{1/4}}=3^{1/4}\times 6^{1/8}=\mathrm{fourth}\mathrm{root}\mathrm{of}3\times \mathrm{eighth}\mathrm{root}\mathrm{of}6$