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

Solution:

i) 2 - √5

The sum or difference between a rational number and an irrational number is always irrational.

Here 2 is a rational number and √5 is an irrational number. Hence 2 - √5 is an irrational number.

ii) (3 + √23) - √23

By simplifying the given expression we get 3.

3 = 3/1, which is in the form of p/q and hence a rational number.

Thus, (3 + √23) - √23 is a rational number.

iii) 2√7 / 7√7

2√7 ÷ 7√7 = 2/7, which is in the form of p/q and hence a rational number.

Thus, 2√7 / 7√7 is a rational number.

iv) 1/√2

1/√2 = (1/√2) × (√2/√2)

= √2/2

= 1.414/2

= 0.702 is a non - terminating, non-recurring decimal which is irrational, and hence 1/√2 is an irrational number.

v) 2π

2π = 2 × 3.1415

π is an irrational number whose value is non-terminating and non-recurring. 2 is a rational number.

The product of a non-zero rational number and an irrational number is always an irrational number.

Hence, 2π is an irrational number.

☛ Check: CBSE Class 9 Maths NCERT Solutions Chapter 1

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Video Solution:

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

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.5 Question 1:

Summary:

2 - √5, 1/√2, and 2π are irrational numbers whereas, (3 + √23) - √23 and 2√7 / 7√7 are rational numbers.

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