Question

Show that if a and b are rational numbers, so is \[(a+\sqrt{b})(a-\sqrt{b})\]

Answer 1

what do you get when you multiply?

Answer 2

a^2-b

Answer 3

ok, then you are one step away from the proof. finish by saying that rational numbers are closed under elementary operations, in this case squaring and subtraction

Answer 4

in other words if \(a\) is rational then so is \(a^2\) and if you subtract a rational number \(b\) from a rational number \(a^2\) then the result it rational as well

Answer 5

cool. thanks