Chapter 1

NCERT
Class 9
Mathematics
Solutions
1. Classify the following numbers as rational or irrational: (i) 2 − √5

Question:

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

Answer:

(i) 2− √5

In the given number 2 is rational number and √5 is irrational number. So, √5 is subtracted from 2. Now subtracting we will get an irrational number.

Hence, 2− √5 is an irrational number.

(ii) (3+ √23)− √23 = 3+ √23− √23 = 3 which is a rational number

(iii) 2√7/ 7√7 = 2/7 which is a rational number

(iv) 1/√2

is irrational number.

Because the quotient of a non-zero rational number with an irrational number is irrational.

(v) 2π

2 is rational number and π is an irrational number. So, we know that the product of a nonzero rational number with an irrational number is irrational.

Hence, 2π is irrational number.

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