# Root and Square of a Number: The Basic Concepts of Mathematics

We deal with numbers every day in the life. Students are taught about numbers from the start of their academics. Numbers are the fundamentals of mathematics. Numbers are everywhere. From looking at the time to noting down the score of the team in sports. Everywhere numbers are there. There are undefined numbers or one can say they are infinite. Many numbers have certain properties with them. One such property associated with numbers is the perfect square. As it is a very common property of numbers. We will be discussing the perfect square and square root in this article. It will help students to grasp the topic more easily.

Perfect square: While dealing with numbers we come across various numbers which are perfect squares. If we multiply any two numbers, then the product, we get is always a perfect square of that number. In simple words, one can define a perfect square as a number that is obtained by squaring the whole number. Let us take an example for a better understanding of the concept. Let us take a number five, now multiply five with itself only then we will get twenty-five. Hence twenty-five is a perfect square. Similarly, let us take the number twenty-three. Now one will find, that there is not even a single integer which when multiplied by its own gives us the value equal to twenty-three. Hence it is clear that twenty-three is not a perfect square.

We need to identify whether a given number is a perfect square or not. There are few observations that one needs to do to find the perfect square. Consider a number 1000 as this number has an odd number of zeros it can’t be a perfect square but if there are even numbers like in the number 100 or 10000 then that is a perfect square. Similarly, there are many more ways to directly predict whether a number is a perfect square or not. Students must know whether a number is a perfect square or not as it is a very common question.

Square root: We can say that a number raised to the power half gives us the square root of that number. One can also say that it is the opposite of squaring a number. Suppose there is a number whose square is known to us and we want to know the number whose square it is. In this case, we will use the square root to get back the original number. For example, consider the number nine. Now, the square root of this number is always equal to 3 as three is the number which, when multiplied by itself, gives us the product as 9. Let us discuss a few methods of calculating the square root of a number.

There are many ways of calculating the square root of a number. We will discuss one of them. Let us take the first method that is the repeated subtraction method of square root. It can be considered the easiest method. In this method, we have to subtract consecutive odd numbers from the number whose square root we are finding. This process is continued until we get the final result as zero. Now we have to count how many times we have subtracted and the sum we get is our result. Take 9 for example. Now subtract 1 from it then 3 after that 5 and we will finally get zero. Here we have subtracted 3 times. Thus, we found out that the square root of 9 is 3.

The above article discusses in detail the perfect square and square root. They are one of the basic concepts of mathematics that every individual should know. If students know the square root of a number or the square of a number then it reduces the time spent on solving the problem to a great extent. Cuemath is a platform that explains such math concepts easily so that students can perform well in mathematics. They explain the toughest of the math concepts in the easiest way. Many students are nowadays ae to use online platforms. Hence, they should use Cuemath to excel in their studies.