To simplify the radical expression $3\sqrt{24}$, follow these steps:

1. Factorize 24:
   $24 = 4 \times 6$ Since $4 = 2^2$, you can express $\sqrt{24}$ as: $\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6}$

2. Simplify the square root of 4:
   $\sqrt{4} = 2$ Therefore: $\sqrt{24} = 2\sqrt{6}$

3. Multiply by the coefficient $3$: $3\sqrt{24} = 3 \times 2\sqrt{6} = 6\sqrt{6}$

Thus, the simplified form of $3\sqrt{24}$ is $\boxed{6\sqrt{6}}$.

Would you like further details or have any questions?

Here are five related questions to explore:

1. How do you simplify $4\sqrt{50}$?
2. What is the simplified form of $7\sqrt{72}$?
3. How would you simplify $5\sqrt{45}$?
4. What is the simplified form of $8\sqrt{18}$?
5. How do you simplify $2\sqrt{98}$?

Tip: When simplifying radicals, always look for perfect square factors of the number under the square root.