Rational and irrational numbers

I would appreciate any comment upon the correctness of the following
assertion:

Consider (1) below
xy = z (1) where x,y,z are real numbers such that z is an
integer,both x and y are irrational.
Assertion: Both x and y must satisfy (2) and (3); (a,b) = 1.
x = sqrt(a)+ sqrt(b) (2) and y = sqrt(a) - sqrt(b) (3)
where atleast one of a or b must be a non-square.

.

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