Express $0.6+0 . \overline{7}+0.4 \overline{7}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.
Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ upto three places of decimal.
$\frac{\sqrt{2}}{2+\sqrt{2}}$
Simplify the following:
$\frac{2 \sqrt{3}}{3}-\frac{\sqrt{3}}{6}$
Divide $12 \sqrt{30}$ by $3 \sqrt{5}$.
Locate $\sqrt{5}, \sqrt{10}$ and $\sqrt{17}$ on the number line.