Question

proof that 2-√3 is irrational

Answer 1

Let 2-√3 be a rational number.

A rational number can be written in the form of p/q.

2-√3 = p/q

√3 = 2-p/q

√3 = (2q-p)/q

p,q are integers then (2q-p)/q is a rational number,

Then √3 is also a rational number.

But this contradicts the fact that √3 is an irrational number.

So,our supposition is false.

Therefore,2-√3 is an irrational number

Hence proved.