# Thread: Prove that you can add and multiply elements...

1. ## Prove that you can add and multiply elements...

Let Z[sqrt(2)] be all the real numbers of the form a + b*sqrt(2) with a and b integers. Prove that you can add and multiply elements in this set and always get elements in the set.

2. Addition is pretty straight forward

Multiplication: $(a+b\sqrt2)(c+d\sqrt2) = ac+2bd+(ad+bc)\sqrt2$