Is zero a rational number ? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$ ?

Rationalise the denominators of the following :

$(i)$ $\frac{1}{\sqrt{7}}$

$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$

$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$

$(iv)$ $\frac{1}{\sqrt{7}-2}$

Show how $\sqrt 5$ can be represented on the number line.

Add $2 \sqrt{2}+5 \sqrt{3}$ and $\sqrt{2}-3 \sqrt{3}$

Find :

$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}$

$(ii)$ $\left(\frac{1}{3^{3}}\right)^{7}$

$(iii)$ $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$

$(iv)$ $7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$

Simplify

$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$

$(ii)$ $\left(3^{\frac{1}{5}}\right)^{4}$

$(iii)$ $\frac{7^{\frac{1}{5}}}{7^{\frac{1}{3}}}$

$(iv)$ $13^{\frac{1}{5}} \cdot 17^{\frac{1}{5}}$