Math Problem Statement
The prime factorization is 3^2 · 5^2. What number does this describe?
Solution
The prime factorization given is .
To find the number it describes:
- Compute .
- Compute .
- Multiply the results: .
Thus, the number described by this prime factorization is 225.
Would you like me to explain any steps further or help with related concepts?
Here are 5 related questions for further exploration:
- What are the prime factors of 225, and how can you verify them?
- Can you rewrite 225 as a product of its prime factors in exponential form?
- How would you calculate , and what are its prime factors?
- Can you determine if another number (e.g., 144) has the same prime structure?
- How can you efficiently find prime factors of larger numbers?
Tip: To verify your prime factorization, always multiply the factors back together to check the result.
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Math Problem Analysis
Mathematical Concepts
Prime Factorization
Exponents
Multiplication
Formulas
a^m · b^n = (a^m) × (b^n)
Theorems
Fundamental Theorem of Arithmetic
Suitable Grade Level
Grades 5-7