Find three rational numbers between $0.1$ and $0.11$.

Which of the following is irrational?

If $a = 2 + \sqrt{3}$,then find the value of $a - \frac{1}{a}$.

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 $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}=a+b \sqrt{35},$ find the value of $a$ and $b$.

Subtract: $0.\overline{52} - 0.4\overline{6}$