The given expression is:

$\sqrt{8} \cdot \sqrt[3]{4}$

Let's break this down:

1. Square root of 8: $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

2. Cube root of 4: $\sqrt[3]{4} = 4^{1/3}$

Now, the expression becomes: $2\sqrt{2} \cdot 4^{1/3}$

This can be left in this form or simplified further, but there isn't a straightforward way to combine these terms unless approximations are used.

Would you like an exact or decimal approximation for the result, or would you like to simplify this expression further?

Here are 5 questions related to this:

1. How do you simplify expressions involving both square roots and cube roots?
2. What properties of exponents can be used to combine roots?
3. Can you express $\sqrt{2}$ and $4^{1/3}$ in decimal form to approximate the product?
4. How does prime factorization help simplify radicals like $\sqrt{8}$?
5. How would the expression change if higher-order roots were involved?

Tip: When dealing with roots, express numbers in terms of their prime factors to simplify the expression.