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

Express $1.23 \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$

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

Represent geometrically numbers on the number line:

$\sqrt{5.6}$

Insert a rational number and an irrational number between the following:

$2$ and $3$

Rationalise the denominator in each of the following

$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$