Question

Prove that 3 is an
erratio nal
number.​

Answer 1

Answer:

hence proved

Step-by-step explanation:

by assuming

Answer 2

Let's assume to the contrary that it is rational .

so , √3 = a/b ( a and b ≠ 0 )

so , b√3 = a

squaring both sides ,

3b² = a²

Therefore , a² is divisible by 3 .

so we can write a = 3c for some integer c .

Substituting for a , we get

3b² = 9c² i.e. b² = 3c²

This means that b² is divisible by 3 and b is also divisible by 3 .

So , a and b have at least 3 as a common factor .

But this contradicts the fact that √3 is rational .

So , √3 is irrational .