# 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

**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.

**☛ Related Questions:**

- Simplify each of the following expressions: (i) (3 + √3)(2 + √2) (ii) (3 + √3)(3 - √3) (iii) (√5 + √2)² (iv) (√5 - √2)(√5 + √2)
- Recall, π is defined as the ratio of circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
- Represent √9.3 on the number line.
- Rationalize the denominators of the following: i) 1/√7 ii) 1/(√7 - √6) iii) 1/(√5 + √2) iv) 1/(√7 - 2)

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