Question

Prove that √3 is an irrational number​

Answer 1

Answer:

Let √3 be a rational number.

Then √3 = q/p ( Assumed )

Squaring both sides --

(√3)² = (q/p)²

3 = p²/ q²

Therefore

3q² = p²

3 divides p² » 3 divides p

Therefore 3 is a factor of p

Now Taking p = 3c

Again 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 q/p is rational.

Hence √3 is an irrational number.

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