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Concise Mathematics Class 8 ICSE Solutions for Chapter 3 - Squares and Square Roots

## ICSE Class 8 Mathematics Chapter 3 Selina Concise Solutions - Free PDF Download

In search of ICSE solutions for Square and Square roots. Your search is completed and you are in the right place.

Vedantu Selina Concise Mathematics Class 8 Solutions Chapter 3 - Square and Square Roots pdf helps students to understand the basic concepts of Square and square roots. Veadntu ICSE Selina Concise Solutions are designed by experts at Vedantu in a very simple and precise format explaining all the necessary concepts included in the latest syllabus quite easily and effectively. For a better understanding of the concepts, students can refer to Vedantu Selina Solutions Concise Maths Class 8 Chapter 3 Square and Square Roots PDF, from the links provided here.

Class 8 Chapter 3 Square and Square Roots will help students to calculate the square and Square Roots of the given number. The Solved examples after every concept help students gain confidence in solving challenging problems based on Square and Square roots. With the help of Vedantu Selina Solutions Concise Maths Class 8 Chapter 3 Square and Square Roots, students will be able to understand the problems more clearly.

These Vedantu solutions for Class 8 ICSE will help students to score good marks in ICSE Exams 2020-21. The solutions are provided by Vedantu in a stepwise manner to help the students get a thorough knowledge of all the fundamentals.

Before solving the problems let us revise the basic concepts of Square and Square Roots.

### Basics of Squares and Square Root

### Square

A product of a number with itself is said to be square or perfect square. Also, you can say that if any number is multiplied by itself it gives a perfect square.

For example, 81 is a perfect square since it can be written as 81 = 9 x 9.

A perfect square is a number obtained by squaring two equal integers.

Suppose, if a given number is a perfect square or not we write the given number as the product of prime factors then we make pairs of the same factors. If there are pair factors, then the given number is a perfect square.

### Properties of Square Numbers

Numbers that end with 2, 3, 7, or 8 can never be a perfect square.

A perfect square can be determined by the number of zeros at the end of it. If a number is ending with an even number of zeros then it must be a perfect square but if a number has an odd number of zeros then it will be a perfect square.

The squares of even numbers will always result in an even number and the squares of odd numbers will always result in odd numbers.

If we square a natural number other than 1, the multiple that we might get will either be a multiple of 3 or will exceed a multiple of 3 by 1.

If we square a natural number other than 1 the multiple that we might get will either be a multiple of 4 or exceeds a multiple of 4 by 1.

The unit of the number of a square of a natural number = the unit’s digit of the square of the digit at the unit's place of the provided natural number.

There are n natural numbers a and b so that a 2 = 2b 2.

For each and every natural number n, (n + 1)2- n2 = ( n + 1) + n.

If a natural number n is larger than 1,

### Square Root

The square root of any given number is that number which when multiplied by itself gives the given number itself. The number is a perfect square.

For Example, 82 =64, or the square root of 64 is 8

132 =269, or the square root of 269 is 13

The symbol of the square root is √

Therefore, the square root of 64 is represented as √ 64 = 8.

And the square root of 269 is represented as √ 269 = 13 and so on.

### Properties of Square Root

If a number has 2,3, 7, and 8 in unit place then it does not have a square root in natural numbers.

If a number has an odd number of zeros at the end, then it does not have a square root in natural numbers.

The square root of an odd number is odd and the even number is even.

Negative numbers have no defined squares root in a set of real numbers.

### Finding Square Roots

To calculate the square root of perfect square numbers, any one of the following methods can be used.

Prime factorization method

Repeated subtraction method

Long division method

Number line method

Average method

But, if the number is not a perfect square prime factorization method and the repeated subtraction method will not be applicable, we have to use other methods for finding the square roots.

### Why Refer Vedantu ICSE Selina Solutions

Students can refer to Vedantu's ICSE Selina Solutions pdf for class 8 chapter 3 Square and Square roots. The Solutions are explained in a proper step-by-step format in a simple language.

### Some of the Important Features of Vedantu Selina ICSE Solutions Are

Vedantu ICSE solutions contain all the necessary tips helpful for accurate solutions.

The solutions are explained in simple language.

Difficult problems are split up into smaller sections to make it easier to solve.

Alternative methods of solving questions are provided for a better understanding of difficult concepts.

Extra questions are provided to test your preparation level.

Vedantu also provides the necessary diagrams, charts, tables, and images where ever necessary making it conceptually clear.

All the solutions are based on the latest ICSE syllabus.

The Vedantu ICSE Solutions are available in PDF format to help the students download these free study material and refer it offline as well. The topic-wise ICSE solutions can be downloaded from the links given below.

The problems are categorized into different exercises based on the topics they belong to, making it easy for the students to solve the questions. Vedantu Selina solutions contain both easy as well as complicated questions to practice, solving which the students will be able to understand the problem-solving method thoroughly.

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