Find the value of $a$ :
$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $y^{2}=9$
$(iii)$ $z^{2}=0.04$
$(iv)$ $u^{2}=\frac{17}{4}$

Arrange the following numbers in ascending order: $\sqrt{3}, \sqrt[3]{4}, \sqrt[4]{10}$

Find the value of the following expression correct to three decimal places,taking $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$:
$\frac{\sqrt{10} - \sqrt{5}}{2}$

Which type of number is the number $\frac{22}{7}$? Is it rational or irrational?

Find the value of $b$ :
$\frac{\sqrt{2}+\sqrt{3}}{3 \sqrt{2}-2 \sqrt{3}}=2-b \sqrt{6}$