Question

prove that (2-7√3) is an irrational number where √3 is irrational.

please help me with this question​

Answer 1

Answer:

Hi let's assume that 2√3-7 is rational

Let,

2√3-7=r, where r is rational

2√3= r+7

√3=r + 7/2

Here,

RHS is purely rational,whereas, LHS is irrational

This is a contradiction.

Hence,

our assumption was wrong.

Therefore,

2√3-7 is an irrational number.