Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$.

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

Visualize $4.\overline{26}$ on the number line,up to $4$ decimal places.

Find:
$(i)$ $2^{2/3} \cdot 2^{1/5}$
$(ii)$ $(1/3^3)^7$
$(iii)$ $11^{1/2} / 11^{1/4}$
$(iv)$ $7^{1/2} \cdot 8^{1/2}$

Show that $0.3333... = 0.\overline{3}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

Are the square roots of all positive integers irrational? If not,give an example of the square root of a number that is a rational number.