Q. 27

Prove that √3 is

Answer :

Let √3 be a rational number.

Then √3 = p/q HCF (p,q) = 1

Squaring both sides

(√3)2 = (p/q)2

3 = p2/ q2

3q2 = p2

3 divides p2 � 3 divides p

3 is a factor of p

Take p = 3C

3q2 = (3c)2

3q2 = 9C2

3 divides q2 � 3 divides q

3 is a factor of q

Therefore 3 is a common factor of p and q

It is a contradiction to our assumption that p/q is rational.

Hence √3 is an irrational number.

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<span lang="EN-USRS Aggarwal - Mathematics