Question

Prove that 5+3root2 is a irrational number

Answer 1

If possible, let us assume 5 + 3 root 2 rational. Then;

(5+3 root 2)-5 = a rational number

or, 3 root 2 = a rational number

or, 3root 2 /3 = a rational number

which means, root 2 = a rational number

This contradicts the fact that root 2 is irrational. The contradiction arises by taking root (5+3 root 2) rational.

Hence, (5+3 root 3) is irrational.

HOPE THIS COULD HELP!!!