Math Problem Statement
Solution
This expression involves multiplying two cube roots:
[ \sqrt[3]{4} \cdot \sqrt[3]{9} ]
To simplify, we can use the property of radicals:
[ \sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b} ]
So:
[ \sqrt[3]{4} \cdot \sqrt[3]{9} = \sqrt[3]{4 \cdot 9} ]
[ \sqrt[3]{4 \cdot 9} = \sqrt[3]{36} ]
The result is:
This is the simplified form, as cannot be simplified further unless we compute its approximate decimal value. Let me know if you'd like me to calculate that or explain further!
Questions to expand your understanding:
- What are the properties of cube roots and how do they differ from square roots?
- How would this expression change if it involved square roots instead of cube roots?
- Can the cube root of 36 be written as a fractional exponent, and what does that represent?
- How can you compute the approximate decimal value of ?
- What are some real-world applications of cube roots in mathematics or physics?
Tip:
Remember that cube roots can handle negative numbers (e.g., ), unlike square roots for real numbers.
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Math Problem Analysis
Mathematical Concepts
Radicals
Cube Roots
Properties of Exponents
Formulas
\(\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}\)
Theorems
Properties of nth roots
Suitable Grade Level
Grades 9-11
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