Question

prove that √3 ia irrational number​

Answer 1

let √3 be rational

√3 = p/q

p = q√3

p² = q² * 3

thus, 3 is a factor of p²

and 3 is a factor of p also

let p = 3k

we know that p = q√3

(3k)² = (q√3)²

9k² = 3q²

3k² = q²

thus, 3 is a factor of q² and q also.

p and q are not co-prime

Thus, √3 is irrational