As a mathematician, one of the most commonly asked question I get is “what is the answer to the square root of 225?”. It is a simple question that often trips many people up due to the fact that they forget or do not understand the fundamental concepts behind square roots. In this article, we will explore the concept of square roots, detail the process for finding the square root of any number, and ultimately provide the answer to the square root of 225.

To begin, let’s establish what a square root is. A square root is a number that when multiplied by itself gives the original number. For example, the square root of 16 is 4 because 4 multiplied by itself equals 16. The symbol used to represent a square root is √, so the square root of 16 can also be written as √16.

Now, let’s move onto the process for finding the square root of any number. The most basic method is through the use of prime factorization. To find the square root of a number, we want to find the two factors that are identical, and multiply them together. For instance, if we wanted to find the square root of 144, we would first find the prime factorization of 144:

144 = 2 × 2 × 2 × 2 × 3 × 3

Next, we group the factors into pairs and take their product:

√144 = √(2 × 2) × √(2 × 2) × √(3 × 3)

Simplifying this expression, we get:

√144 = 2 × 2 × 3

√144 = 12

Thus, the square root of 144 is 12. This method works for any number, no matter how large or small.

Now, let’s apply this method to find the answer to the square root of 225. First, we find the prime factorization of 225:

225 = 3 × 3 × 5 × 5

Next, we group the factors into pairs and take their product:

√225 = √(3 × 3) × √(5 × 5)

Simplifying this expression, we get:

√225 = 3 × 5

√225 = 15

Thus, the answer to the square root of 225 is 15.

It is important to note that there are alternative methods for finding the square root of a number, such as using a calculator, but the basic process outlined above remains the same. Furthermore, it is also worth mentioning that there are two answers to the square root of a number, one positive and one negative. For example, the square root of 16 can be either 4 or -4, since both 4 and -4 multiplied by themselves equal 16. However, when dealing with non-negative real numbers, we only refer to the positive square root.

In conclusion, the answer to the square root of 225 is 15. By understanding the fundamental concepts behind square roots and using the basic method of prime factorization, we can find the answer to the square root of any number. While there may be alternative methods for finding square roots, the basic process remains the same, and is a useful tool for mathematicians and non-mathematicians alike.