To simplify the cube root of $135$, we factorize $135$ into its prime factors:

1. Prime factorization of $135$: $135 = 3 \times 45 = 3 \times 3 \times 15 = 3 \times 3 \times 3 \times 5 = 3^3 \times 5$

2. Take the cube root of $135$: Using the property of cube roots, $\sqrt[3]{a^3 \cdot b} = a \cdot \sqrt[3]{b}$: [ \sqrt[3]{135} = \sqrt[3]{3^3 \cdot 5} = 3 \cdot \sqrt[3]{5} ]

Final Simplified Form:

[ \sqrt[3]{135} = 3\sqrt[3]{5} ]

Would you like a deeper explanation or details about cube roots? 😊

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Related Questions:

1. How do you find the cube root of a decimal or fractional number?
2. What is the difference between square roots and cube roots?
3. Can cube roots of negative numbers be simplified in the same way?
4. How do you approximate cube roots for numbers that are not perfect cubes?
5. Are there any special cases or properties for higher-order roots?

Tip: Always start by checking if the given number is a perfect cube to simplify quickly!