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

Classify the following numbers as rational or irrational :

$(i)$ $2-\sqrt{5}$

$(ii)$ $(3+\sqrt{23})-\sqrt{23}$

$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}}$

$(iv)$ $\frac{1}{\sqrt{2}}$

$(v)$ $2 \pi$

Are the following statements true or false ? Give reasons for your answers.

$(i)$ Every whole number is a natural number.

$(ii)$ Every integer is a rational number.

$(iii)$ Every rational number is an integer.

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.

Show how $\sqrt 5$ can be represented on the number line.

Classify the following numbers as rational or irrational :

$(i)$ $\sqrt{23}$

$(ii)$ $\sqrt{225}$

$(iii)$ $0.3796$

$(iv)$ $7.478478 \ldots$

$(v)$ $1.101001000100001 \ldots$