Question

prove that 2√3-7 is an irrational number

Answer 1

Let us assume that 2root3-7 is rational.
Then 2 root 3 - 7 = a/b where a and b are rationals
arranging the equation we get root 3 = (ab + 7 ) * 1/2
Now since rhs = rational so root 3 should be rational. 
But this contradicts the fact in reality that root 3 is irrational . So our assumption is wrong and hence 2 root 3-7 is irrational.

Answer 2

Hi !!

Lets 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