Hello please could you tell me if my proof that the sqrt of 4 is irrational is correct.

therefore so ....1.1

This implies that a is greater than b and that a is even.

a is even so a=2k

put into 1.1

cancel by 4

this can be written as this implies that which implies that ....1.2

Equation 1.2 contradicts equation 1.1. This shows that a and b cannot be whole positive integers.