Find an irrational number between $\frac{1}{7}$ and $\frac{2}{7}$. (in $...$)

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

State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number.

Rationalise the denominator of $\frac{1}{7+3 \sqrt{2}}$

Find the values of:
$(i)$ $64^{\frac{1}{2}}$
$(ii)$ $32^{\frac{1}{5}}$
$(iii)$ $125^{\frac{1}{3}}$

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