Math Problem Statement
Simplify the cube root of 343, \( \sqrt[3]{343} \).
Solution
To simplify , we need to determine whether 343 has any perfect cube factors.
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Prime Factorization of 343:
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Cube Root Simplification: [ \sqrt[3]{343} = \sqrt[3]{7^3} ]
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The cube root of simplifies to:
Thus, the simplified form of is .
Would you like further details or have any other questions?
Here are some related questions to expand your understanding:
- What is the process for simplifying cube roots of larger numbers?
- How do cube roots differ from square roots in terms of simplification?
- What are the cube roots of other powers of 7, like ?
- Can you explain how to estimate cube roots for non-perfect cubes?
- How do prime factorizations help in simplifying roots?
Tip: Always check for perfect cubes when simplifying cube roots.
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Math Problem Analysis
Mathematical Concepts
Simplification
Roots
Cube Roots
Formulas
\( \sqrt[3]{a^3} = a \)
Theorems
Properties of Exponents and Roots
Suitable Grade Level
Grades 8-10