Final answer:
To find the product of √4(√8 + 3), we simplify the square root of 4 to 2 and distribute it across the parentheses, leading to 2√8 + 6 which is simplified to 4√2 + 6. The correct answer cannot be precisely determined from the provided choices due to possible typos.
Step-by-step explanation:
To find the product of √4(√8 + 3), we will follow several steps. First, we need to simplify the square roots. The square root of 4 is 2. Next, we distribute the 2 across the sum inside the parentheses:
2 * (√8 + 3) = 2√8 + 2*3 = 2√8 + 6
Now we can simplify 2√8. The square root of 8 is equivalent to the square root of 4 times 2, which is 2√2. Thus, 2√8 simplifies to 2*2√2 = 4√2. Finally, we can rewrite the expression:
4√2 + 6
Looking at the answer choices, we can see that none of them precisely match our simplified expression. However, because √2 is approximately 1.414, we could represent 4√2 as approximately 4 * 1.414, which is approximately 5.656. Therefore, the correct choice is closest to 5.656 + 6, which is approximately 11.656. It appears there might be a typo or mistake either in the question or the answer choices as provided.