Please forgive my unimagianative question, but is x2=2y2 possible if both x and y are rational numbers?
Not possible......to see why let x = a/b and let y = c/d where a,b,c,d are integers
Then we have that
(a/b)^2 = 2(c/d)^2 rearrange as
(a/b)^2 /(c/d)^2 = 2
(a^2 *d^2) / (b^2 *c^2) = 2 take the square root of both sides
(a * d) / (b * c) = √2
But a*d , b*c are both integers.......let a*d = m and b*c = n
m / n = √2
But......the square root of two is irrational....so.....we're led to a false conclusion.....thus, x and y are not both rational