Question

prove that root 3 is an irrational number​

Answer 1

Answer:

√3 is an irrational number (given)

Let √3 be rational number

√3 = a/b (where a and b are coprime)

Squaring on both side

(√3)² = (a/b)²

3 = a²/b²

a² = 3b², b² = a²/3____(i)

So, 3 divides a²

Then, 3 also divides a

let a = 3c,

b² = a²/3

b² = 9c²/3

b² = 3c²

c²= b²/3_______(ii)

From equation (i) and (ii),

3 is also a factor of a and b.

It contradict the fact that no common factor of a and b other than 1.

Hence, √3 is an irrational number.

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