Class10 NCRT Real Numbers Exercise – 1.3 pdf || UP Board

 Real Numbers
Exercise – 1.3

 

1. Prove that √5 is irrational.

Solution:

Let√5 is a rational number.

So 5 will divide b², Therefore 5 will divide b .…………(iii)

Now, Equations (i) and (ii) show that a and b have a common factor of 5 which is contrary to our assumption (since a and b are co-prime numbers i.e. a and b have no common factor other than 1.)

So this contradiction proves that contrary to our imagination, √5 is an irrational number.

2. Prove that 3+2√5 is irrational.

Solution:

Let 3+2√5 is rational

However, we know that √5 is an irrational number, So this contradiction proves that contrary to our imagination, 3+2√5 is an irrational number.

 

3. Prove that the following are irrationals:

 

(ii) 7√5

Solution:

Let 7√5 is rational

However, we know that √5 is an irrational number, So this contradiction proves that contrary to our imagination, 7√5 is an irrational number.

 

(iii) 6+√2

Solution:

Let 6+√2 is rational

However, we know that √2 is an irrational number, So this contradiction proves that contrary to our imagination, 6+√2 is an irrational number.

 Download Class10 NCRT Real Numbers  Exercise – 1.3 pdf