Rewrite cube root of, 192, end cube root 
3
  
192
​
  in simplest form.

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.

Rewrite cube root of 192 in simplest form.

Learn how to simplify the cube root of 192 through prime factorization and properties of cube roots. This solution breaks down 192 into prime factors and applies cube root properties to simplify it into 4 cube root of 3. Perfect for students in Grades 8-10 learning about cube roots and algebra.

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