Simplify each of the following expressions:
(i) $(3 + \sqrt{3})(2 + \sqrt{2})$

Simplify each of the following expressions:
(ii) $(3 + \sqrt{3})(3 - \sqrt{3})$

Represent $\sqrt{9.3}$ on the number line.

Rationalise the denominators of the following:
(ii) $\frac{1}{\sqrt{7} - \sqrt{6}}$

Simplify each of the following expressions:
(iii) $(\sqrt{5} + \sqrt{2})^2$

Rationalise the denominators of the following:
(i) $\frac{1}{\sqrt{7}}$

Recall, $\pi$ is defined as the ratio of the circumference (say $c$) of a circle to its diameter (say $d$). That is, $\pi = \frac{c}{d}$. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?

Classify the following numbers as rational or irrational:
(v) $2\pi$

Classify the following numbers as rational or irrational:
(iv) $\frac{1}{\sqrt{2}}$

Classify the following numbers as rational or irrational:
(i) $2 - \sqrt{5}$

Rationalise the denominators of the following:
(iv) $\frac{1}{\sqrt{7} - 2}$

Rationalise the denominators of the following:
(iii) $\frac{1}{\sqrt{5} + \sqrt{2}}$

Classify the following numbers as rational or irrational:
(ii) $(3 + \sqrt{23}) - \sqrt{23}$

Simplify each of the following expressions:
(iv) $(\sqrt{5} - \sqrt{2})(\sqrt{5} + \sqrt{2})$

Classify the following numbers as rational or irrational:
(iii) $\frac{2\sqrt{7}}{7\sqrt{7}}$