prove that the square root of 2 plus the square root of 3 is not rational?
does always the sum of two not rational numbers is a not rational number?
i know the proof 2 = a^2/b^2
i separately proved that square root of 2 and square root of 3 are irrational
how two prove that the sum of two such numbers is irrational too?
i will try to prove by contradiction:
(2)^0.5 + (3)^0.5 is a rational number
(if we multiply a rational number by a rational number we will get a rational number "h")
5+2*(2)^0.5 * (3)^0.5=h
24=h^2 -10*h +25
h^2 -10*h +1=0
by this rational roots theorem
the possible roots is +1 and -1
not one of the represent the actual roots of h^2 -10*h +1=0
what is the next step in the prove?