Question

Prove that (2-√3) is a irrational number

Answer 1

Proof:Let us assume that 2-√3 is is a rational number.

=> it should be in the form of p/q (fraction)

=> 2-√3 = p/q

= √3 = p/q + 2q/q

But we know that √3 is an irrational number. It contradicts our assumption that 2-√3 is a rational number.

Therefore 2-√3 is an irrational number.