Question

prove that 2+root 3 is irrational ​

Answer 1

answer :-

let 2+√3 is a rational number.

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

2+√3 = p/q

√3 = p/q - 2

√3 = (p-2q) /q

p and q are integers , then (p-2q) / q is 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.