Math Problem Statement
Solution
The problem requires simplifying the cube root of 147, written as .
To simplify this expression, let’s analyze if 147 can be broken down into factors that include a perfect cube:
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The prime factorization of 147 is:
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Since none of the factors form a perfect cube (like , , , etc.), the expression cannot be simplified further in terms of whole numbers or integers.
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Therefore, the simplest form of this expression is:
So, the answer to enter is:
Would you like further explanation on cube roots or prime factorization?
Here are some additional related questions to consider:
- What are the general steps for simplifying cube roots?
- How do you find the prime factorization of a number?
- Can cube roots of numbers that aren’t perfect cubes be expressed as exact decimals?
- How would this simplification differ if it were a square root instead of a cube root?
- Are there any practical applications of cube roots in real-life situations?
Tip: When simplifying roots, always check if the number can be factored into powers matching the root (like cubes for cube roots) for easier simplification.
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Math Problem Analysis
Mathematical Concepts
Cube Root
Prime Factorization
Formulas
Cube Root Simplification \( \sqrt[3]{a} \)
Theorems
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Suitable Grade Level
Grades 8-10