Question

1. Classify the following numbers as rational or irrational:
(1) 2-√5
(i) (3 + √23) - √23 (ii
2√7/
7√7
(iv)1/√2
(v) 2π​

Answer 1

1) 2 - √5 is irrational because difference

of a rational number 2 and an irrational number√5 is an irrational number

2) ( 3 + √23 ) - √23

= 3 + √23 - √23

= 3, a rational number

3) 2√7/7√7

= 2/7 × √7/√7

= 2/7, a rational number

4) 1/√2 is irrational because when we divide a rational number 1 by an irrational number √2 we get an irrational number

5) 2π is irrational because product of a rational number 2 and irrational number

π is an irrational number