Question

prove that √3 is an irrational number by the method of contradiction​

Answer 1

Answer:

We have E. D lemma has

a=bq+r

Assume that root3 is rational number

root3=p/q

squaring in both sides

root3²=p²/q²

3. =p²/q²

3q² =p²

3 is a factor of p²

3 is also a factor of p

Take p=3m²

3q²=9m²

q² =3m²

3 is a factor of q²

3 is also factor of p

So root3 has p and q has factors so by our contradiction root3 is irrational