What is the square root of 225

General
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what is the square root of 225

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What is the square root of 225?

Answer: The square root of 225 is a fundamental mathematical calculation. To find the square root, you need to determine what number, when multiplied by itself, equals 225.

Mathematically, this is represented as:

\sqrt{225}

To solve this, you can either use factorization or recognize common perfect squares.

Factorization Method:

  1. Prime Factorization of 225:

    • Divide 225 by the smallest prime number that can divide it evenly.

    • 225 is divisible by 3:

      225 \div 3 = 75

    • 75 is also divisible by 3:

      75 \div 3 = 25

    • 25 is divisible by 5:

      25 \div 5 = 5

    • 5 is divisible by 5:

      5 \div 5 = 1

    • So, the prime factorization of 225 is:

      225 = 3^2 \times 5^2

  2. Taking the Square Root:

    • To find the square root, take the square root of each prime factor:

      \sqrt{225} = \sqrt{3^2 \times 5^2} = 3 \times 5 = 15

Recognizing Perfect Squares:

  • 225 is a perfect square because it can be expressed as the square of an integer:

    225 = 15^2

  • Therefore, the square root of 225 is:

    \sqrt{225} = 15

Conclusion:

The square root of 225 is \boxed{15}.