Prove that 2 is an irrational number

1.	Prove that 2 is an irrational number
Answer» Let root 3 is rational number. root3 =p/q ( where, p and q are integer , q is not equal to 0 and p and q are co-primes ).root 3q = p.Squaring both sides.3p2=q2 (q square and p square)...... (i).3 divides p2.3 divides p.......... (ii).p2 = 3q2.p2 =3m.Put the value of p2.p2=3q2.(3m)2=3q2.9m2=3q2.3m2=q2.q2=3m2.3 divides q2.3 divides q.......... (iii).By eqn (ii) and (iii) 3 divides p and 3 divides also q.3 is the common factor of p and q. This is contradiction because our assumption is wrong. Hence, root 3 is irrational number. 2 or root 2

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