Q.1. Classify the following numbers as rational or irrational:

Solution:

(i) = 2 - 2.2360679… = - 0.2360679…

2 is rational and $\sqrt{5}$ is irrational.

Since the number (2 - $\sqrt{5}$) involves subtraction of a irrational number from a rational number, it is an irrational number.

(ii)

Since the number can be represented in $\frac{\mathrm{p}}{\mathrm{q}}$ form, it is a rational number.

$\left(\mathrm{i}\mathrm{i}\mathrm{i}\right)\frac{2\sqrt{7}}{7\sqrt{7}}=\frac{2}{7}$

Since the number can be represented in $\frac{\mathrm{p}}{\mathrm{q}}$  form, it is a rational number.

Since the number involves, division of an irrational number by a rational number, it is an irrational number.

(v) 2π = 2 × 3.1415… = 6.2830…

π is an irrational number. Since the number involves, multiplication of an irrational number with a rational number, it is an irrational number.