Squares and Square Roots Class 8 Notes CBSE Maths Chapter 5|Free PDF Download

Definition:

Squares of the Numbers from 1 to 20

1. Square: 

Number obtained when a number is multiplied by itself is called square of that number.

The numbers are expressed as ${{n}^{2}}$ where $n$ is an integer. It is read as the number raised to the power $2$.

For example: square of $3$ is ${{3}^{2}}=3\times 3=9$.

Properties of Square of A Number:

• If a natural number m can be expressed as ${{n}^{2}}$, where $n$ is also a natural number, then m is called a square number.

• Every square number ends with \[0,\text{ }1,\text{ }4,\text{ }5,\text{ }6\text{ }\]or $9$ at unit’s place.

• Square numbers can only have even number of zeros at the end.
  
  

2. Square Root:

Square root is the inverse operation of squaring a number.

A perfect square number has two integral square roots.

Positive square root of a number is denoted by the symbol $\sqrt{{}}$.  For example, $\sqrt{4}=2$ but not $-2$.

Properties of Square Number: 

i) A number that ends with $2,3,7$ or $8$ is never a perfect square. For example: $32,63,77$etc.

ii) A number ending in \[0,\text{ }1,\text{ }4,\text{ }5,\text{ }6\text{ }\]or $9$ may or may not be a square number. Example: $34,35,46$etc.

iii) Square of even number is even. For example, ${{6}^{2}}=36$ and square of odd number is odd. For example, ${{3}^{2}}=9$.

iv) A number that is ending with an odd number of zeroes cannot be a perfect square. For example: $130,1000,100000$ etc.

v) The difference between the squares of two consecutive natural number is always equal to their sum \[{{\left( n\text{ }+\text{ }1 \right)}^{2}}-\text{ }{{n}^{2}}=\text{ }n+1+n\]. For example: ${{5}^{2}}-{{4}^{2}}=5+4=9$.

vi) For any natural number \[m(>1)\], if \[{{(2m)}^{2}}+\text{ }{{({{m}^{2}}-\text{ }1)}^{2}}=\text{ }{{({{m}^{2}}+\text{ }1)}^{2}}\] , then \[{{(2m)}^{2}},\text{ }{{({{m}^{2}}-\text{ }1)}^{2}},{{({{m}^{2}}+\text{ }1)}^{2}}\]  forms a Pythagorean triplet. For example: \[{{4}^{2}}+{{3}^{2}}={{5}^{2}}\] where $m=2$.

Maths Chapter 5 Class 8 Squares and Square Roots – At a Glance

In this chapter, you will learn about square numbers and square roots. After practising this chapter, students will understand how a natural number m can be expressed as n2 where n is a natural number too. This chapter will also show you how to calculate square roots - the inverse operation of a square.

Going through our revision notes on Class 8 Maths Chapter 5 will help you to gain a comprehensive understanding of this chapter. Our notes come with straightforward language to help you memorise the steps and formulas within this chapter. It is an initiative from the in-house team of experts who have an in-depth idea about the chapter and of student psychology.

While the notes are as per the latest NCERT guidelines, the easy-to-read language makes it a viable option to follow up on the details of the chapter sans being overwhelmed with the same. 

We maintain a high standard and accuracy to help students who refer to them achieve high grades. You can download Square and Square Roots Class 8 Notes PDF to go through them at your leisure for a smooth revision process.

Chapter 5 Class 8 – Revision Notes

Our Square and Square Roots Class 8 Notes, explains the crucial concepts from this chapter in short keynotes. Our revision notes have divided the ideas in following sub-heads so that you can have a quick look-through before your exams.

1. Square

Under this section from Chapter 5 of Class 8 Maths, you will be able to revise that a square number is obtained when a number is multiplied by itself. It has been explained with an example in our revision notes. Go through the sample to form a clear idea of this section.

2. Square Number or Perfect Square

You can review your understanding of perfect square under this section by following up with our Class 8 Maths Chapter 5 Notes.

3. Properties of Square Number

Read through this section to revise the features of square numbers before your exams. This section will help you to quickly clarify how the square of even numbers turns out to be even. It also explains that the difference of squares of two consecutive natural numbers is equal to their sum.

Benefits of Referring to the Revision Notes for CBSE Class 8 Maths Chapter 5 — Squares and Square Roots

You can find below the benefits of the revision notes for CBSE Class 8 Maths Chapter 5 — Squares and Square Roots. 

• These notes will clear your concepts related to the Square and Square Roots chapter. 

• By referring to these notes, students will be able to solve all questions asked in the NCERT exercise and also answer the questions in the exam confidently.

• The topics are covered in precise and easy-to-understand language. They are well-structured and also comprise bullet points.

• These notes are created by the subject matter experts with in-depth understanding of the topics covered.

• These revision notes are error-free and are prepared by keeping in mind the student’s need for faster and efficient revision of chapters without leaving out vital information.

• It enables students to effectively prepare their topics in less time and even on the night before the exam. The notes come with solved questions to enable them to test their knowledge.

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