Math Problem Statement

The prime factorization is 3^2 · 5^2. What number does this describe?

Solution

The prime factorization given is 32523^2 \cdot 5^2.

To find the number it describes:

  1. Compute 32=93^2 = 9.
  2. Compute 52=255^2 = 25.
  3. Multiply the results: 925=2259 \cdot 25 = 225.

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:

  1. What are the prime factors of 225, and how can you verify them?
  2. Can you rewrite 225 as a product of its prime factors in exponential form?
  3. How would you calculate 2252225^2, and what are its prime factors?
  4. Can you determine if another number (e.g., 144) has the same prime structure?
  5. 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