# Classify the following numbers as rational or irrational:

i) √23 ii) √225 iii) 0.3796 iv) 7.478478... v) 1.101001000100001...

**Solution:**

i) √23

√23 = √23/1 = p/q, but p is not an integer.

Hence √23 is an irrational number.

ii) √225

√225 = 15/1 = p/q, where p and q are integers and q ≠ 0.

Hence √225 is a rational number.

iii) 0.3796

0.3796 is a rational number because it is a terminating decimal number.

iv) 7.478478...

7.478478... is a rational number as it is a non-terminating recurring decimal i.e, the block of numbers 478 is repeating.

v) 1.101001000100001 . . . .

It is an irrational number because it is a non-terminating and non-recurring decimal.

**Video Solution:**

## Classify the following numbers as rational or irrational: i) √23 ii) √225 iii) 0.3796 iv) 7.478478... v) 1.101001000100001...

### NCERT Solutions Class 9 Maths - Chapter 1 Exercise 1.3 Question 9:

**Summary:**

√23, 1.101001000100001... are irrational numbers whereas √225, 0.3796, and 7.478478... are rational numbers.