CBSE Class 8 Maths Revision Notes Chapter 6

CBSE Class 8 Mathematics Revision Notes Chapter 6 – Squares And Square Roots

In these Class 8 Mathematics Chapter 6 Notes, students will learn about squares and square roots. In addition, in these Class 8 Chapter 6 Mathematics Notes, students will get to know the significant details of the chapter that are important for their final examination. Along with Chapter 6 Mathematics Class 8 Notes, Extramarks will provide students with essential questions that can be asked to prepare them quickly. Moreover, Class 8 Mathematics Notes Chapter 6 will be a student’s last-minute revision guide, providing all the necessary information. These notes are based on the CBSE Syllabus.

Squares of the Numbers from 1 to 20

12 = 1 112 = 121
22 = 4 122 = 144
32 = 9 132 = 169
42 = 16 142 = 196
52 = 25 152 = 225
62 = 36 162 = 256
72 = 49 172 = 289
82 = 64 182 = 324
92 = 81 192 = 361
102 = 100 202 = 400


The number obtained when a number is multiplied by itself is called the square of that number. The numbers are expressed as n2, where n is the integer. It is referred to as the number raised to power 2. For example, the square of 3 is 32=3×3=9.

Properties of Square of a Number

If a natural number p can be expressed as q2, where q is also a natural number, then p is called a square number. Every square number ends with 0, 1, 4, 5, 6, or 9 at the unit’s place. Square numbers will only have an even number of zeros at the end.

Square Root

The square root is the inverse operation of squaring a number. A perfect square number consists of two integral square roots. The symbol denotes the positive square root of a number √. For example, 4=2 but not −2.

Properties of Square Number

  1. i) A number that has 2,3,7, or 8 at the end will never be a perfect square. For example, 32,63,77, etc.
  2. ii) A number that has 0, 1, 4, 5, 6, or 9 may or may not be a square number. Example: 34,35,46 etc.

iii) Square of the even number is even. For example,62 =36, and the square of an odd number is odd. For example, 32=9.

  1. iv) A number that ends with and that has zeros in an odd number will not be a perfect square. For example, 130,1000,100000, etc.
  2. v) The difference of the squares of two consecutive natural numbers is always equal to their sum n+12n2= n+1+n. For example 5242= 5 + 4= 9
  3. vi) A natural number where m(>1), if 2m2 + (m2-1)2= (m2+1)2 , then 2m2, (m2-1)2, and  (m2+1)2 forms a Pythagorean triplet. For example: 42+32=52   where m=2.

Revision Notes For CBSE Class 8 Mathematics Chapter 6 – Free PDF Download

Access Class 8 Mathematics Chapter 6 – Squares And Square Roots

Mathematics Chapter 6 Class 8 Squares And Square Roots – At A Glance

In these Class 8 Chapter 6 Notes, students will learn about squares and square roots. After practising this chapter, students will learn how a natural number n can be expressed as n2, where n is a natural number. This chapter will also teach you how to calculate square roots – the inverse operation of a square. These notes are based on CBSE Syllabus and NCERT Books. 

If you go through our CBSE Revision Notes on Class 8 Mathematics Chapter 6, they will help you to gain a comprehensive understanding of this chapter. Our notes come with simple language to help you memorise the steps and Formulas within this chapter and also provide Important Questions that can come up in your examination. It is an initiative taken by our in-house team of experts who have an in-depth idea of the chapter and psychology of a student. Once you have gone through our Class 8 Chapter 6 Notes, you can easily solve all the CBSE Past Years’ Question Papers.

While the notes are made as per the latest NCERT Books guidelines, the simple language makes it a viable option to follow up on the details of the chapter without being overwhelmed. 

We keep a high standard and accuracy to help students who refer to them achieve good grades. Download Square and Square Roots Class 8 Notes PDF to read them at your convenience for a smooth revision process.  These notes also contain CBSE Extra Questions that will help students test their understanding.

Chapter 6 Class 8 – Revision Notes

These Square and Square Roots Class 8 Revision Notes explain the crucial concepts from this chapter in short keynotes. Our revision notes have divided the ideas into the following sub-heads so that you can have a quick go through them before your examination.

  1. Square

Beneath this section from Chapter 6 of Class 8 Mathematics, you will be able to recall that a square number is obtained when a number is multiplied by itself. It has been illustrated with an example in our notes. Go through the sample to get a clear idea of this section. After revising these notes, you can easily solve CBSE Sample Papers.

  1. Square Number or Perfect Square

You can review your understanding of the perfect square under this section by going through our Class 8 Mathematics Chapter 6 Notes.

  1. Properties of Square Number

This part will help you quickly understand how the square of even numbers turns out to be even. It also explains that the difference between the squares of two consecutive natural numbers is equal to their sum. 

Advantages of Referring to the Revision Notes for CBSE Class 8 Mathematics Chapter 6 — Squares and Square Roots:

  • These notes will help you clarify your concepts related to the Square and Square Roots chapters. By referring to these notes, students can solve all the questions asked in the NCERT exercise and answer the questions in the exam confidently.
  • The topics covered are precise and in simple language. They consist of bullet points and are well-structured.
  • The subject matter experts have created these notes with an in-depth understanding of the topics covered.
  • These revision notes are free of errors and prepared by keeping in mind the student’s need for faster and more efficient revision of chapters without missing any vital information.
  • It helps students with their preparation for their exams in less time. The notes contain solved questions to enable students to test their knowledge.

FAQs (Frequently Asked Questions)

1. What is the square root?

A square root is a number that produces the same result when multiplied by itself. For instance, 7 is the square root of 49 because 49 is the result of multiplying 7 by 7.

2. What are the patterns used to find the square of a number?

Some patterns followed to find the square of a number is as follows:

  • Triangular number addition
  • A number between square numbers.
  • Adding an odd number 
  • A sum of consecutive natural numbers
  • Product of two consecutive even or odd numbers
  • Some more patterns in square numbers.

3. What are perfect squares? Give an example.

The numbers whose square root gives a whole number are called perfect squares. For example, the number 16 is a perfect square because its root is a whole number, i.e.,√16 = 4.

4. What is an imperfect square with examples?

A number whose square root gives a fraction is called an imperfect square. The value derived by taking the square root of the imperfect square can be non-terminating.

For example, 2 is an imperfect square as its root is equal to,

√2 = 1.414, which is a fraction.

5. Is there a difference between square and square roots?

The primary difference between them is that the square root of a number gives the root of a number that has been squared.