Use the factor method to find the square root of 225

1 answer

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 \( \boxed{15} \).