Squares And Square Roots

The squares and square roots hold a great significance in mathematics especially for kids in higher grades. The concept of squares and square roots is applied in various math topics and is vital in preparing for competitive studies. The core knowledge of square and square 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 concept of square roots 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 Squares and Square Roots:

Definition of Squares:

Squares are the numbers, generated after multiplying a number by itself. It is the inverse of a square root. For example, the square of 4 is 16 and the square root of 16 is 4. Similarly, square of 5 is 25  and square root of 25 is 5.

How to find Squares?

The Square of a number can be found by multiplying a number by itself. For single-digit numbers, we can use multiplication tables to find the square, while in the case of two or more than two-digit numbers, we perform multiplication of the number by itself to get the answer. For example,11×11 = 121, where 121 is the square of 11. 

Definition of Square Roots: 

The square root of numbers is a value 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

Repeated Subtraction Method 

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.

Square root by using Prime Factorization


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

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