Simplify the radical expression.
2√6 + 3√96
2√6 + 3√96 = 2√6 + 3√(16*6) = 2√6 + 3√16 * √6 = 2√6 + 3(4)√6 = 2√6 + 12√6 = (2+12)√6 = 14√6. Answer: \boxed{14\sqrt{6}}.
To simplify the radical expression 2√6 + 3√96, we want to look for any perfect square factors that are common between 6 and 96.
First, we will break down 6 and 96 into their prime factorization:
6 = 2 * 3
96 = 2^5 * 3
Now, let's identify the common perfect square factors:
The perfect square factors of 6 are 2 and 3.
The perfect square factors of 96 are 2^2 = 4 and 3.
Since both numbers have a perfect square factor of 2 and a perfect square factor of 3, we can simplify the expression:
2√6 + 3√96 = 2√2 * √3 + 3√4 * √24
= 2√2 * √3 + 3 * 2 * √6
= 2√2 * √3 + 6√6
Therefore, the simplified form of the radical expression 2√6 + 3√96 is 2√2 * √3 + 6√6.