NCERT Solutions for Class 8 Maths Squares and Square Roots Ex 6.3

NCERT Solutions for Class 8 Maths Squares and Square Roots Ex 6.3 are a free study guide for every student. These solutions help you understand how to solve questions related to finding square roots, the repeated subtraction method, and the prime factorisation method. This exercise includes 10 questions whose step by step solutions are included in our NCERT solutions PDF. All these solutions are created by our Maths experts and are based on the latest CBSE exam pattern and syllabus. 

You can download NCERT Class 8 Maths Solutions for Squares and Square Roots Ex 6.3 for free from the askIITians website. This way you can practice problem solving at your convenience and schedule. Finding the square root of a number comes in handy in many competitive exams and helps you master basic mathematical skills. Let us see what’s included in exercise 6.3 of Class 8 Maths Squares and Square Roots. 

About NCERT Class 8 Maths Chapter 6 Exercise 6.3

Important properties of the square root of a number include:

• The Square root of an even perfect square is even and that of an odd Perfect square is odd.
• Since there is no number whose square is negative, the square root of a negative number is not defined.
• If a number ends with an odd number of zeroes, then it cannot have a square root which is a natural number.
• If the unit digit of a number is 2, 3, 7 or 8 then the square root of that number (in natural numbers) is not possible.
• If m is not a perfect square, then there is no integer n such that the square root of m is n.

Square root using repeated subtraction: 

We know that the sum of the first n odd natural numbers is n2. That is, every square number can be expressed as a sum of successive odd natural numbers starting from 1. So, to find the square root of a number using repeated subtraction, you just have to subtract odd numbers from it until you obtain a 0. The step at which you obtain a zero marks the square root of the number. 

The square root of a number using prime factorisation: 

In this method, you have to find the prime factorisation of the given number whose square root is to be calculated. You will see that each prime factor occurs at least twice if the given number is a perfect square. Then, you have to pair up the repeating prime numbers and find the square root of the number in the following ways:

Suppose you have to find the square root of 225

The prime factorisation of 225 = 5 X 5 X 3 X 3 

So, 225 = 5 X 5 X 3 X 3

225 =  (5)² X (3)²

225 = 5 X 3 = 15 

So, the square root of 225 is 15. 

Download NCERT Solutions for Class 8 Maths Squares and Square Roots Ex 6.3

NCERT Solutions for Class 8 Maths are important for every student because: 

1. They are self-explanatory and help you understand how to solve the questions of the exercise. 
2. They are based on the latest exam pattern and syllabus given by CBSE so they are a great learning tool for exam preparation. 
3. They include stepwise answers so they are easy to understand. 
4. They are 100% reliable as they are prepared by askIITians experts who have years of experience in teaching Class 8 Maths students. 
5. You can download these solutions for free and refer to them whenever you want. 

There are different types of questions included in NCERT Solutions for Class 8 Maths Squares and Square Roots Ex 6.3. These include: 

• Ex 6.3 Q1: Finding the possible ‘one’s’ digits of the square root of the given numbers. 
• Ex 6.3 Q2: Estimating which of the given numbers are not perfect squares. 
• Ex 6.3 Q3 and Q4: Finding square roots of numbers using repeated subtraction and prime factorization. 
• Ex 6.3 Q5: Finding the smallest whole number that should be multiplied with a number to make it a perfect square. You will be required to use the prime factorisation method here. 
• Ex 6.3 Q6: Finding the smallest whole number that should be divided with the given number to make it a perfect square.
• Ex 6.3 Q7 and Q8: This is a word problem type question where you have to apply the concept of finding the square root using prime factorisation. 
• Ex 6.3 Q9 and Q10: Finding the smallest square number that is divisible by the given numbers. 

Download our NCERT Solutions today to know how to solve each of these questions of squares and square roots. 

NCERT Solutions for Class 8 Maths Squares and Square Roots Ex 6.3 FAQs

1. What are the important topics included in NCERT Class 8 Maths Squares and Square Roots Ex 6.3?

Exercise 6.3 of the Class 8 Maths Squares and Square Roots chapter includes important topics like finding the square root of a number using the repeated subtraction method and the prime factorisation method. 

2. Are there any other study resources available for Class 8 Maths Chapter Squares and Square Roots? 

Yes, askIITians provides the full study package for Class 8 Maths squares and square roots. This includes revision notes, daily practice questions, sample papers, mock tests and previous year questions. We also provide flashcards and mind maps for interactive learning of the concepts. 

3. How many exercises are there in the NCERT Class 8 Maths Squares and Square Roots Chapter? 

There are 4 exercises in NCERT Class 8 Maths Squares and Square Roots Chapter. Exercise 6.1 has 9 Questions, Exercise 6.2 has 2 Questions, Exercise 6.3 has 10 Questions and Exercise 6.4 has 9 Questions. In total, there are 30 questions in this chapter.