To rewrite the expression $\sqrt[3]{24}$ in simple radical form, we first factorize 24 into its prime factors:

$24 = 2^3 \times 3$

Now, substitute this into the cube root:

[ \sqrt[3]{24} = \sqrt[3]{2^3 \times 3} ]

Since the cube root of $2^3$ is $2$, we can simplify the expression:

[ \sqrt[3]{24} = 2 \times \sqrt[3]{3} = 2\sqrt[3]{3} ]

So, the simplified radical form is:

$\boxed{2\sqrt[3]{3}}$

Would you like further details or have any questions? Here are five related questions:

1. How would you simplify $\sqrt[3]{54}$?
2. What is the simplified radical form of $\sqrt[4]{80}$?
3. Can you express $\sqrt[3]{108}$ in simple radical form?
4. How would you simplify $\sqrt[5]{96}$?
5. What is the general method for simplifying any cube root expression?

Tip: Always start by factorizing the number under the radical into its prime factors to simplify the expression effectively.