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

i 2 - 5      ii 3 + 23- 23

iii 2777        iv 12     v 2π

Solution:

(i) 2 - 5 = 2 - 2.2360679… = - 0.2360679…

2 is rational and 5 is irrational.

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

(ii) 3 + 23- 23=3 + 23- 23

= 3 = 31

Since the number can be represented in pq form, it is a rational number.

iii2777=27

Since the number can be represented in pq  form, it is a rational number.

iv 12 = 22= 0.7071067811

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.