The Basics of Square Roots and Cube Roots

The topic of square roots and cube roots holds a great significance in mathematics especially for kids in higher grades. It is applied in various important topics essential in preparing for competitive exams. The core knowledge of square and cube roots is crucial for various advanced topics based on them. Since the topic is foundational for acquiring a variety of math skills, it is therefore essential for students to master this topic. 

The Basics of Square Roots and Cube Roots
[ image: pexels by pixabay ]

The concept of square and cube roots is often used in formulas of the quadratic and cubic equations, exponents, and to find the area and volume of geometric objects. In particular, square roots are often seen in mathematical formulas, as well as in many physical laws. The quadratic fields and rings of quadratic integers, which are based on square roots, are important in algebra and have their use in geometry. Cube roots are used to solve cubic equations. It can also be used to solve for the dimensions of a three-dimensional object of a certain volume.

Introduction to Square Roots and Cube Roots:

Definition of Square Roots: The square root of numbers is a multiple of that number which when multiplied by itself gives the original number. The square root of any given number is inverse to its square. For example, 16 is the square of 4, and 4 is the square root of 16.

How to determine the square root of a number?

Finding the square root of a number that is a perfect square is easy. The square root of such numbers can be calculated by using the following methods: 

● Repeated Subtraction Method

● Square root by using Prime Factorization 

The repeated subtraction method is one of the simplest ways to find the square root of a number. In this method, we subtract the consecutive odd numbers from the given number, till we reach 0. The number of times we subtract the odd number from this number is the square root of the given number. This method is suitable to find the square root of perfect square numbers. For example: Let us find the square root of 9 using this method. 

Step1: Subtract the first odd number from 9 i.e, 9 - 1 = 8,

Step2: Subtract the next odd number from the result of the previous step. i.e, 8 - 3 = 5,

Step3: Subtract the next odd number which is 5 from the result. i.e, 5 - 5 = 0 

Since the count of consecutive subtraction is 3, therefore the square root of 9 is 3. 

Definition of Cube Roots: The cube roots of a number is a multiple of that number which when multiplied thrice to itself gives the original number. It is inverse to the cube of a number and can be obtained by using factorization. For example, 8 is the cube of 2, and 2 is the cube root of 8.

How to determine the cube root of a number?

The cube root of a number can be found by using the prime factorization method. Steps to be followed to find the cube root of a number using the prime factorization method: 

Step 1- Do the prime factorization of the given number.

Step 2- Divide the factors obtained into three groups containing the same number of each factor.

Step 3- Multiply the factors in any one of the groups. That number will be your answer. 

If there is any factor left that cannot be divided equally into three groups, that means the given number is not a perfect cube.

Finding the cube root and square root of a number with the help of a calculator maybe just a task of few clicks. But learning the methods and techniques to find the square and cube roots are handy in learning some basic math skills and for some algebra about cube numbers.