To simplify $\sqrt[3]{192}$, we start by factoring 192:

$192 = 2^6 \times 3$

Now, apply the cube root:

[ \sqrt[3]{192} = \sqrt[3]{2^6 \times 3} = \sqrt[3]{2^6} \times \sqrt[3]{3} ]

Since $\sqrt[3]{2^6} = 2^2 = 4$, the expression becomes:

$4 \times \sqrt[3]{3}$

Thus, $\sqrt[3]{192}$ in its simplest form is:

$4 \sqrt[3]{3}$

Would you like a more detailed breakdown, or have any further questions?

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Here are 5 related questions:

1. How do you factor numbers to simplify roots?
2. What is the difference between square roots and cube roots?
3. How do you simplify higher roots like fourth or fifth roots?
4. How can you convert cube roots into decimal form?
5. How do cube roots apply in geometry, specifically for volumes?

Tip: When simplifying roots, always factor numbers completely to identify perfect cubes, squares, or higher powers.