Multiply $6 \sqrt{5}$ by $2 \sqrt{5}$.

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?

Classify the following numbers as rational or irrational :

$(i)$ $\sqrt{23}$

$(ii)$ $\sqrt{225}$

$(iii)$ $0.3796$

$(iv)$ $7.478478 \ldots$

$(v)$ $1.101001000100001 \ldots$

Find an irrational number between $\frac {1}{7}$ and $\frac {2}{7}$

Check whether $7 \sqrt{5}, \,\frac{7}{\sqrt{5}}, \,\sqrt{2}+21, \,\pi-2$ are irrational numbers or not.

Show that $0.2353535 \ldots=0.2 \overline{35}$ can be expressed in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.