An impossible relation

In the accompanying article on Tangrams, a claim was made that it is not possible to find integers a and b which make any of the following equalities true: √6 = a+b√2, √7 = a+b√2, √12 = a+b√2, and so on. However, the proofs may not be obvious. In this brief note, we shall prove the impossibility of the first relation and leave the remaining ones for you to handle.
18068 registered users
6931 resources