Math Problem Statement
\sqrt{9}\cdot\sqrt[3]{9}
Solution
The expression combines a square root and a cube root of . Here's the detailed calculation:
Expression:
Step 1: Evaluate each root separately.
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: The square root of is , because .
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: The cube root of is the number such that . This is left in its radical form as:
Step 2: Multiply the results.
The product is: [ \sqrt{9} \cdot \sqrt[3]{9} = 3 \cdot \sqrt[3]{9} ]
Final Answer:
Would you like further explanations or to see this in another form (like decimal approximation)?
Related Questions:
- How do square and cube roots differ in their applications?
- Can be simplified further or approximated numerically?
- What is the geometric interpretation of square and cube roots?
- How would this calculation change if it were ?
- What happens if we multiply ?
Tip:
Square and cube roots can often be combined using the rule of exponents: .
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Math Problem Analysis
Mathematical Concepts
Square Roots
Cube Roots
Radicals
Basic Arithmetic Operations
Formulas
Square root: \( \sqrt{a} \) represents the non-negative number whose square is \(a\).
Cube root: \( \sqrt[3]{a} \) represents the number whose cube is \(a\).
Radical multiplication: \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \) (if both are square roots).
Theorems
Rules of Radicals
Suitable Grade Level
Grades 8-10