Add $2 \sqrt{2}+5 \sqrt{3}$ and $\sqrt{2}-3 \sqrt{3}$
$3 \sqrt{2}+2 \sqrt{3}$
$2 \sqrt{3}+3 \sqrt{2}$
$2 \sqrt{2}+2 \sqrt{2}$
$3 \sqrt{3}+3 \sqrt{3}$
Rationalise the denominator of $\frac{1}{\sqrt{2}}$.
Find six rational numbers between $3$ and $4$.
Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
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 $q \neq 0$.
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?