Divide $8 \sqrt{15}$ by $2 \sqrt{3}$

State whether the following statements are true or false. Justify your answers.

$(i)$ Every irrational number is a real number.

$(ii)$ Every point on the number line is of the form $\sqrt m$ , where $m$ is a natural number.

$(iii)$ Every real number is an irrational number.

Find six rational numbers between $3$ and $4$.

Write the following in decimal form and say what kind of decimal expansion each has :

$(i)$ $\frac{36}{100}$

$(ii)$ $\frac{1}{11}$

$(iii)$ $4 \frac{1}{8}$

$(iv)$ $\frac{3}{13}$

$(v)$ $\frac{2}{11}$

$(vi)$ $\frac{329}{400}$

Are the square roots of all positive integers irrational ? If not, give an example of the square root of a number that is a rational number.

Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.