Question
Use the factor method to find the square root of 225
Answers
GPT-4o mini
To find the square root of 225 using the factor method, we start by factoring 225 into its prime factors.
1. **Divide by the smallest prime number:**
- 225 is an odd number, so we start with 3.
- \( 225 \div 3 = 75 \)
2. **Continue factoring the result:**
- Now factor 75: \( 75 \div 3 = 25 \)
3. **Factor 25:**
- Continue with 25: \( 25 \div 5 = 5 \)
- And then: \( 5 \div 5 = 1 \)
4. **We can list the prime factors:**
- So, we have \( 225 = 3 \times 3 \times 5 \times 5 \), or \( 225 = 3^2 \times 5^2 \).
5. **To find the square root, take one of each pair of prime factors:**
- \(\sqrt{225} = \sqrt{3^2 \times 5^2} = 3 \times 5 = 15\).
Thus, the square root of 225 is \( \boxed{15} \).
1. **Divide by the smallest prime number:**
- 225 is an odd number, so we start with 3.
- \( 225 \div 3 = 75 \)
2. **Continue factoring the result:**
- Now factor 75: \( 75 \div 3 = 25 \)
3. **Factor 25:**
- Continue with 25: \( 25 \div 5 = 5 \)
- And then: \( 5 \div 5 = 1 \)
4. **We can list the prime factors:**
- So, we have \( 225 = 3 \times 3 \times 5 \times 5 \), or \( 225 = 3^2 \times 5^2 \).
5. **To find the square root, take one of each pair of prime factors:**
- \(\sqrt{225} = \sqrt{3^2 \times 5^2} = 3 \times 5 = 15\).
Thus, the square root of 225 is \( \boxed{15} \).