Answer:
To simplify the given expression, we can first break down the numbers under the square roots into their prime factorization.
The prime factorization of 54 is 2 * 3^3, and the prime factorization of 24 is 2^3 * 3.
Using this, we can simplify the expression:
3√54 + 2√24 = 3√(2 * 3^3) + 2√(2^3 * 3)
= 3√(2 * 3 * 3 * 3) + 2√(2 * 2 * 2 * 3)
= 3√(2^1 * 3^2) * √3 + 2√(2^1 * 2^2) * √3
= 3 * 3√(2^1 * 3^2) + 2 * 2√(2^1 * 2^2) * √3
= 9√(2 * 3^2) + 4√(2^2 * 3)
= 9√(2 * 9) + 4√(4 * 3)
= 9√(2) * √9 + 4√(4) * √3
= 9√2 * 3 + 4√3 * 2
= 27√2 + 8√3
Therefore, the simplified expression is 27√2 + 8√3.
None of the answer choices given match this expression, so the correct option is e) None of these.
Explanation: