Final answer:
The two fissionable materials retrieved from spent nuclear fuel rods during fuel reprocessing are plutonium and americium.
Step-by-step explanation:
Plutonium-239 and americium-241 are both transuranium elements that can be used as fuel in nuclear reactors.
During reprocessing, the spent fuel rods are dissolved in acid, and various chemical processes are used to separate the different components. Plutonium and americium are separated from the other components and can be reused as fuel in a process called nuclear recycling.
Plutonium-239 is particularly valuable because it can undergo fission in a similar way to uranium-235, the most commonly used fuel in nuclear reactors. Americium-241 can be used as a source of neutrons in certain types of nuclear reactors. So therefore the two fissionable materials that are retrieved from spent nuclear fuel rods during fuel reprocessing are plutonium and americium.