Find the square root by prime factorization method \[13225\].

Hint:
The method of prime factorization is used to “break down” or express a given number as a product of prime numbers. If a prime number occurs more than once in the factorization, it is usually expressed in exponential form so that we can use it up according to our need.

Complete step by step solution:
Given below is the prime factorization method for \[13225\].

Prime factorization of 13225 \[ = 5 \times 5 \times 23 \times 23\]
\[
   \Rightarrow \sqrt {13225} = \sqrt {5 \times 5 \times 23 \times 23} \\
   \Rightarrow \sqrt {13225} = 5 \times 23 \\
   \Rightarrow \sqrt {13225} = 115 \\
\]

Square root of 13225= 115.

Note:
For such questions, you can easily verify your answer just by squaring the square root.
Example: \[115 \times 115\]=13225.
Hence, our answer is verified.