X^4-256=0 numbers of rational roots

x = 8 or x = -8

Step-by-step explanation:

x^4 - 256 = 0

<=>x^4 - 4^4 = 0

<=>(x - 8)(x + 8)(x^2 + 64) = 0

Case 1 :

x - 8 = 0

<=>x = 8 (choose)

Case 2:

x + 8 = 0

<=>x = -8 (choose)

Case 3:

x^2 + 64 = 0

<=>x^2 = -64 (nonsense)

so x = 8 or x = -8

Done :))