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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?

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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.

Simplify the expression \( \sqrt{8} \cdot \sqrt[3]{4} \)

Learn how to simplify the expression \( \sqrt{8} \cdot \sqrt[3]{4} \) using properties of radicals and exponents. Explore the breakdown of square roots and cube roots, and apply relevant formulas for solving the expression. Suitable for students in Grades 9-10.

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