Question

prove that


prove that √7
is an irrantional number​

Answer 1

OK. PLEASE MAKE ME BRAINLIEST AND FOLLOW ME

Answer 2

Let us assume that

√7

is rational. Then, there exist co-prime positive integers a and b such that

√7 =a/b

⟹a=b /

7

Squaring on both sides, we get

a

2

=7b

2

Therefore, a

2

is divisible by 7 and hence, a is also divisible by7

so, we can write a=7p, for some integer p.

Substituting for a, we get 49p

2

=7b

2

⟹b

2

=7p

2

.

This means, b

2

is also divisible by 7 and so, b is also divisible by 7.

Therefore, a and b have at least one common factor, i.e., 7.

But, this contradicts the fact that a and b are co-prime.

Thus, our supposition is wrong.

Hence,

√7 is irrational.