Show that uder root 2 is …

First of all we have that under root 2 is rational Under root2=a/b in which a and b are. co-prime Now, b under root 2= a, So, by squaring both the sides we have, 2b square=a square Therefore, by using theorem 1.3 we have that if 2 divides 'a 'square so then, 2 divides 'a'.So, we have, a=2c (for some integer c) So, by substituting a, we get 2b square =4c square. Now, shift 2 on other side so we get, b square= 2c square. So, again by theorem 1.3 we have that, 2 divides b square so it also so 2 also divides b. So, this occurs because of our wrong assumption so, we conclude that under 2 is not rational but it is irrational