For each question,select the proper option from four options given,to make the statement true: $(5^{-2})^{3} = \ldots \ldots \ldots$

If $\sqrt{2} = 1.4142$,then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to

Find three different irrational numbers between the irrational numbers $\sqrt{2}$ and $\sqrt{5}$.

Rationalise the denominator of the following expression and evaluate it by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$,and $\sqrt{5}=2.236$ up to three decimal places:
$\frac{\sqrt{2}}{2+\sqrt{2}}$

If $a = 5 + 2\sqrt{6}$ and $b = \frac{1}{a}$,then what will be the value of $a^2 + b^2$?

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