Final answer:
The simplification of 12√8 in radical form is 24√2. This is done by converting 8 into its prime factors (2*2*2), taking out one 2 from the square root, and multiplying the 12 to get 24√2.
Step-by-step explanation:
To simplify the radical expression 12√8, we must first break 8 into its prime factors. The prime factorization of 8 is 2*2*2 or 2³.
In square roots, we look for pairs of the same numbers. There are indeed two 2s, which means we can take one 2 out of the square root. We multiply the 2 by the 12 to get 24. So, 12√8 simplifies to 24√2.
Therefore, our simplified radical form is 24√2, which corresponds to option (b) in your list of choices.
Learn more about Simplifying Radicals