Let us assume that 4 is rational, then it can be expressed in the form of qp where p,q have no factors in common, thus qp=4. or p2/q2=4 then p2=4q2, with p has a factor of 4. Let p=4m, then (4m)2=4q2→16m2=4q2,4m2=q2, then q also has a factor of 4. But this contradicts the fact that p,q are coprimes. Thus the assumption that 4 is rational is wrong. Hence, 4 is also irrational.
This concludes that 4=2 is an irrational number.
Which of these above colored equations are not necessarily correct?