Question

3. Prove that each of the following numbers is irrational:
(i) √6​

Answer 1

Answer:

let us suppose that √6 is rational number.

There exist two co-prime numbers , say p and q

So

6

=

q

p

Squaring both sides , we get

6=

q

2

p

2

..(1)

Which shows that ,p

2

is divisible by 6

this implies , p is divisible by 6

Let p=6a for some integer a

Equation (1) implies = 6q

2

=36a

2

⇒q

2

=6a

2

q

2

is also divisible by 6

⇒q is divisible by 6

6 is common factors of p and q

but this contradicts the fact that p and q have no common factor.

our assumption is wrong thus √6is irrational

Answer 2

Hope This will help you ।।।।