Square Root of 225 by Prime Factorization

Another method for calculating the square root of 225 is the prime factorization method. As the name suggests, this method involves writing down all the prime factors of a number. Let us see how.

Step 1: Take the number whose square root is to be calculated and generate all its prime factors. Prime factors are the numbers whose divisors are 1 and the number itself. For 225, the prime factors will be

225= 3 x 3 x 5 x 5

Step 2: Now, we are required to match the prime factors, the pairs formed have the same numbers. Note that it is only possible if the number has an even number of prime factors. For 225, pairs

225= (3 x 3) x (5 x 5)

Step 3: After generating the pairs, take the square roots on both sides to calculate the square root of the original number. For 225,

√225= √(3 x 3) x √(5 x 5

√225= 3 x 5

√225= 15

Therefore, the square root of 225 is the number 15.

Note: This method is only useful for Perfect Square and Numbers containing small radicals values.

The square root of any number after exponentiation gives the original value. The square root of 225 is represented using the under root as √225 or it can also be denoted by writing the half power of the number as (225)^1/2.

In this article, we will study the value of the square root of 225 and examine two different methods to calculate the square root value of 225. We will also discuss the nature of the square root of 225.