Question

1) Prove that √3:is irrational

2) Prove that √7 is irrational

3) Prove that √10 is irrational

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Answer 1

Answer:

Let √3 be a rational number.

Then √3 = q/p

HCF (p,q) =1

Squaring both sides (√3)2 = (q/p)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 qpqp is rational.

Hence √3 is an irrational number