Question

prove that root 5-root 3 is not a rational number

Answer 1

Let be rational

Hence where a and b are integers and b≠ 0.



Squaring on both the sides, we get







Clearly RHS is a rational number as are integers. Whereas LHS is irrational since is irrational.

This is a contradiction.

Hence our assumption that is rational is incorrect.

Therefore is irrational.

Answer 2

$\bold{Answer}$

See the attachment which I attached.

Hope You will understand