Find three rational numbers between
$\frac{5}{7}$ and $\frac{6}{7}$
$\frac{5}{7}=\frac{5}{7} \times \frac{10}{10}=\frac{50}{70}$ and $\frac{6}{7}=\frac{6}{7} \times \frac{10}{10}=\frac{60}{70}$
$\Rightarrow \frac{51}{70}, \frac{52}{70}, \frac{53}{70}$ are three rational numbers lying and between $\frac{50}{70}$ and $\frac{60}{70}$ and therefore lie between $\frac{5}{7}$ and $\frac{6}{7}$
Express $0 . \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$
Add $: 0 . \overline{35}+0 . \overline{28}$
Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$
State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.
Multiply $3 \sqrt{7}$ and $5 \sqrt{7}$.