If $a = \frac{\sqrt{5}}{8}$ and $\frac{8}{a} = b \sqrt{5}$,then find the value of $b$.

Rationalise the denominator in each of the following:
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$

Prove that,$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}=1$.

Multiply $3 \sqrt{7}$ and $5 \sqrt{7}$.

If $x = 3 + 2\sqrt{2}$,then find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{3} + \frac{1}{x^{3}}$.

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........