# Square And Cube Roots – Basic Concepts Of Mathematics We deal with different properties of numbers in mathematics. Many of them are crucial for every student to understand and memorize. As most of them have daily life applications, and they play a crucial role in competitive exams. The cube root of a number and square root of a number is two such critical properties that every student should master as they are widely used in many subjects. Let us discuss both of these properties in detail.

## Cube Root

We all have studied multiplication and other operations. Many numbers show some unique properties. Cube root is a unique property, and not every number has a cube root. To understand cube root, we need to first get to know in detail about the cube of a number. Whenever a number is multiplied three times by its own, then the result, we get is the cube of that number. For example, let us take the number 4. Now multiply 4 by its own, that is 4, we will get 16. Again, repeat the process, multiply 16 by 4, then we will get 64. Thus, we can say that when 4 is multiplied three times by its own it will give us 64 as the output. Hence, 64 is the cube of 4.

Now, as we have got to know what a cube of a number is, let us move to the cube root of a number. The cube root of a given number is the number, which when multiplied by its value three times gives us the given number. Let’s take another example for better understanding. Let the number be 125, and we are told to find the cube root of the number. In such a case we will try to find a number, which when multiplied three times by its own gives us 125. Like in this example, 5 is the cube root of 125 as when we multiply 5 three times by 5 only, we will get 125 as the final product. Not every number has a cube root, like 10 it does not have a whole number as the cube root, there is not a single integer, which when multiplied three times gives us 10. Hence it is a unique property and students should know the cube roots of a few of the basic numbers.

### Square Root

Before discussing cube root, let us know about the square of a number. Whenever a number is multiplied twice by its own, then the result, we get is the square of the number. Suppose 10 is the number, now if we multiply 10 by 10 only, then we will get the final result as 100. Thus, we will say that 100 is the square of 10. Now, the square root of a given number is the number that must be multiplied twice by itself to get the given number. If we are asking to find the square root of any number, let’s say 16. Then we will search for a number that can be multiplied twice by its to give 16 as the result. In this case, 4 will be our answer as to when 4 is multiplied by 4, we will get the final result as 16. Not all the numbers have an integer as a square root. For example, 5 does not have an integer as a square root. A student should memorize the squares and the square root of a few numbers that are constantly asked in exams.

In the above article, we have discussed two of the crucial topics of mathematics. Cube root and square root both are integral parts of students’ daily mathematics. Hence if students face any difficulty in solving them, they should take the help of Cuemath. It is an online platform that offers quality education to students.