The decimal expansion of the number $\sqrt{2}$ is

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5} \times \sqrt{5}$ is a / an $\ldots \ldots \ldots$ number.

Simplify $: \frac{(25)^{\frac{3}{2}} \times (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times (8)^{\frac{4}{3}}}$

Simplify: $\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}$

Simplify:
$(\frac{3}{5})^4 \times (\frac{3}{5})^{-12} \times (\frac{3}{5})^{6}$

Calculate the sum: $0. \overline{3} + 0.4 \overline{7}$