Question

prove that 5 + 2 root 3 is an irrational number

Answer 1

HI !

Let's assume that 5 + 2√3 = r , where "r" is rational

2√3 = r - 5

√3 = r-5/2

Here , we can see that the RHS is purely rational , whereas LHS is irrational.

This leads to a contradiction . Hence, our assumption was wrong.

Therefore, 

5 + 2√3 is irrational. 

Answer 2

,if it is asked for 3 or 4 marks then u will have to first prove
$\sqrt{3}$
Is irrational. But for two marks this much is enough