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# NCERT Solutions for Class 8 Maths Chapter 6: Squares and Square Roots - Exercise 6.3

Last updated date: 29th May 2024
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## NCERT Solutions for Class 8 Maths Chapter 6 (EX 6.3)

NCERT Solutions for Class 8 Maths are provided by Vedantu. Our updated PDF solutions guide answers all the questions in the latest NCERT exercise book for the subject. You will find broadly described and simplified steps in the solution guide that help you understand the problems instead of just providing the solution. The PDF can be freely downloaded from Vedantu’s website and can go a long way to improve your chances for scoring well in your CBSE Class 8 Maths exam. Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.

 Class: NCERT Solutions for Class 8 Subject: Class 8 Maths Chapter Name: Chapter 6 - Squares and Square Roots Exercise: Exercise - 6.3 Content-Type: Text, Videos, Images and PDF Format Academic Year: 2024-25 Medium: English and Hindi Available Materials: Chapter WiseExercise Wise Other Materials Important QuestionsRevision Notes

### Exercise 6.3 of Squares and Square Roots is based on the following topics:

1. Finding square roots

The square root of a number is the inverse operation of squaring a number. The square of a number is the value acquired by multiplying it by itself, whereas the square root of a number is the factor of a number that produces the original number when multiplied by itself. If 'x' is the square root of 'y’, it means that x × x = y.

Note: Finding the square root of a perfect square number is simple. Positive numbers which can be expressed as the product of two numbers are known as perfect squares. Perfect squares are the positive numbers which can be expressed as the product of a number by itself. In simple words, Perfect squares are the numbers which can be expressed as the value of power 2 of any number.

2. Finding square root through repeated subtraction

In this method, we subtract the consecutive odd numbers from the number for which we want to find the square root, till we get the resultant value as 0. The number of times we subtract will be the square root value of the given number. This method is only applicable for perfect square numbers.

3. Finding square root through prime factorisation

Prime factorization of a number is to express that number as a product of prime factors. Steps to be followed to find the square root of a given number through the prime factorization method are:

• Firstly, divide the given number into its prime factors.

• Next, form pairs of similar factors in such a way that both factors in each pair are equal.

• Take one factor from each pair.

• Then, find the product of the factors that are obtained by taking one factor from each pair.

• The product value is equal to the square root of the given number.

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## Access NCERT Solutions for Class 8 Maths Chapter 6 – Squares and Square Roots

Exercise 6.3

1. What could be the possible ‘one’s digits of the square root of each of the following numbers?

i. $\text{9801}$

Ans: We know that the one’s digit of the square root of the number ending with  $1$ can be $1$ or $9$.

Thus, the possible one’s digit of the square root of $9801$ is either $1$ or $9$.

ii. $\text{99856}$

Ans: We know that the one’s digit of the square root of the number ending with  $6$ can be $6$ or $4$.

Thus, the possible one’s digit of the square root of $99856$ is either $6$ or $4$.

iii. $\text{998001}$

Ans: We know that the one’s digit of the square root of the number ending with  $1$ can be $1$ or $9$.

Thus, the possible one’s digit of the square root of $998001$ is either $1$ or $9$.

iv. $\text{657666025}$

Ans: We know that the one’s digit of the square root of the number ending with $5$ will be $5$.

Thus, the only possible one’s digit of the square root of $657666025$ is $5$.

2. Find the numbers which are surely not perfect squares without doing any calculations.

i. $\text{153}$

Ans: The perfect square of numbers may end with any one of the digits $0$, $1$, $4$, $5$, $6$, or $9$. Also, a perfect square has an even number of zeroes at the end of it, if any.

We can see that $153$ has its unit place digit as $3$.

Hence, $153$ cannot be a perfect square.

ii. $\text{257}$

Ans: The perfect square of numbers may end with any one of the digits $0$, $1$, $4$, $5$, $6$, or $9$. Also, a perfect square has an even number of zeroes at the end of it, if any.

We can see that $257$ has its unit place digit as $7$.

Hence, $257$ cannot be a perfect square.

iii. $\text{408}$

Ans: The perfect square of numbers may end with any one of the digits $0$, $1$, $4$, $5$, $6$, or $9$. Also, a perfect square has an even number of zeroes at the end of it, if any.

We can see that $408$ has its unit place digit as $8$.

Hence, $408$ cannot be a perfect square.

iv. $\text{441}$

Ans: The perfect square of numbers may end with any one of the digits $0$, $1$, $4$, $5$, $6$, or $9$. Also, a perfect square has an even number of zeroes at the end of it, if any.

We can see that $441$ has its unit place digit as $1$.

Hence, $441$ is a perfect square.

3. Find the square roots of $\text{100}$ and $\text{169}$ by the method of repeated subtraction.

Ans: It is already known to us that the sum of the first n odd natural numbers is n2.

For $\sqrt{100}$

1. $100-1=99$

2. $99-3=96$

3. $96-5=91$

4. $91-7=84$

5. $84-9=75$

6. $75-11=64$

7. $64-13=51$

8. $51-15=36$

9. $36-17=19$

10.  $19-19=0$

After subtracting successive odd numbers from $1$ to $100$ , we are getting a $0$ at the 10th step.

Hence, $\sqrt{100}=10$

For $\sqrt{169}$

1. $169-1=168$

2. $168-3=165$

3. $165-5=160$

4. $160-7=153$

5. $153-9=144$

6. $144-11=133$

7. $133-13=120$

8. $120-15=105$

9. $105-17=88$

10. $88-19=69$

11.  $69-21=48$

12.  $48-23=25$

13.  $25-25=0$

After subtracting successive odd numbers from $1$ to $169$, we are getting a $0$ at the 13th step.

Hence, $\sqrt{169}=13$

4. Find the square roots of the following numbers by the Prime Factorisation Method.

i. $\text{729}$

Ans:

The factorization of $729$ is as follows:

 $3$ $729$ $3$ $243$ $3$ $81$ $3$ $27$ $3$ $9$ $3$ $3$ $1$

$729=\underline{3\times 3}\times \underline{3\times 3}\times \underline{3\times 3}$

$\sqrt{729}=3\times 3\times 3$

So, $\sqrt{729}=27$

ii. $\text{400}$

Ans: The factorization of $400$ is as follows:

 $2$ $400$ $2$ $200$ $2$ $100$ $2$ $50$ $5$ $25$ $5$ $5$ $1$

$400=\underline{2\times 2}\times \underline{2\times 2}\times \underline{5\times 5}$

$\sqrt{400}=2\times 2\times 5$

So, $\sqrt{400}=20$

iii. $\text{1764}$

Ans:

The factorization of $1764$ is as follows:

 $2$ $1764$ $2$ $882$ $3$ $441$ $3$ $147$ $7$ $49$ $7$ $7$ $1$

$1764=\underline{2\times 2}\times \underline{3\times 3}\times \underline{7\times 7}$

$\sqrt{1764}=2\times 3\times 7$

So, $\sqrt{1764}=42$

iv. $\text{4096}$

Ans: The factorization of $4096$ is as follows:

 $2$ $4096$ $2$ $2048$ $2$ $1024$ $2$ $512$ $2$ $256$ $2$ $128$ $2$ $64$ $2$ $32$ $2$ $16$ $2$ $8$ $2$ $4$ $2$ $2$ $1$

$4096=\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}$

$\sqrt{4096}=2\times 2\times 2\times 2\times 2\times 2$

So, $\sqrt{4096}=64$

v. $\text{7744}$

Ans: The factorization of $7744$ is as follows:

 $2$ $7744$ $2$ $3872$ $2$ $1936$ $2$ $968$ $2$ $484$ $2$ $242$ $11$ $121$ $11$ $11$ $1$

$7744=\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{11\times 11}$

$\sqrt{7744}=2\times 2\times 2\times 11$

So, $\sqrt{7744}=88$

vi. $\text{9604}$

Ans: The factorization of $9604$ is as follows:

 $2$ $9604$ $2$ $4802$ $7$ $2401$ $7$ $343$ $7$ $49$ $7$ $7$ $1$

$9604=\underline{2\times 2}\times \underline{7\times 7}\times \underline{7\times 7}$

$\sqrt{9604}=2\times 7\times 7$

So, $\sqrt{9604}=98$

vii. $\text{5929}$

Ans: The factorization of $5929$ is as follows:

 $7$ $5929$ $7$ $847$ $11$ $121$ $11$ $11$ $1$

$5929=\underline{7\times 7}\times \underline{11\times 11}$

$\sqrt{5929}=7\times 11$

So, $\sqrt{5929}=77$

viii. $\text{9216}$

Ans: The factorization of $9216$ is as follows:

 $2$ $9216$ $2$ $4608$ $2$ $2304$ $2$ $1152$ $2$ $576$ $2$ $288$ $2$ $144$ $2$ $72$ $2$ $36$ $2$ $18$ $3$ $9$ $3$ $3$ $1$

$9216=\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{3\times 3}$

$\sqrt{9216}=2\times 2\times 2\times 2\times 2\times 3$

So, $\sqrt{9216}=96$

ix. $\text{529}$

Ans: The factorization of $529$ is as follows:

 $23$ $529$ $23$ $23$ $1$

$529=\underline{23\times 23}$

So, $\sqrt{529}=23$

x. $\text{8100}$

Ans: The factorization of $8100$ is as follows:

 $2$ $8100$ $2$ $4050$ $3$ $2025$ $3$ $675$ $3$ $225$ $3$ $75$ $5$ $25$ $5$ $5$ $1$

$8100=\underline{2\times 2}\times \underline{3\times 3}\times \underline{3\times 3}\times \underline{5\times 5}$

$\sqrt{8100}=2\times 3\times 3\times 5$

So, $\sqrt{8100}=90$

5. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained.

i. $\text{252}$

Ans: The factorization of $252$ is as follows:

 $2$ $252$ $2$ $126$ $3$ $63$ $3$ $21$ $7$ $7$ $1$

Here, $252=\underline{2\times 2}\times \underline{3\times 3}\times 7$

We can see that $7$ is not paired

So, we have to multiply $252$ by $7$ to get a perfect square.

The new number will be $252\times 7=1764$

$1764=\underline{2\times 2}\times \underline{3\times 3}\times \underline{7\times 7}$

$\sqrt{1764}=2\times 3\times 7$

So, $\sqrt{1764}=42$

ii. $\text{180}$

Ans: The factorization of $180$ is as follows:

 $2$ $180$ $2$ $90$ $3$ $45$ $3$ $15$ $5$ $5$ $1$

Here, $180=\underline{2\times 2}\times \underline{3\times 3}\times 5$

We can see that $5$ is not paired

So, we have to multiply $180$ by $5$ to get a perfect square.

The new number will be $180\times 5=900$

$900=\underline{2\times 2}\times \underline{3\times 3}\times \underline{5\times 5}$ which is a perfect square

$\sqrt{900}=2\times 3\times 5$

So, $\sqrt{900}=30$

iii. $\text{1008}$

Ans: The factorization of $1008$ is as follows:

 $2$ $1008$ $2$ $504$ $2$ $252$ $2$ $126$ $3$ $63$ $3$ $21$ $7$ $7$ $1$

Here, $1008=\underline{2\times 2}\times \underline{2\times 2}\times \underline{3\times 3}\times 7$

We can see that $7$ is not paired

So, we have to multiply $1008$ by $7$ to get a perfect square.

The new number will be $1008\times 7=7056$

$7056=\underline{2\times 2}\times \underline{2\times 2}\times \underline{3\times 3}\times \underline{7\times 7}$ which is a perfect square

$\sqrt{7056}=2\times 2\times 3\times 7$

So, $\sqrt{7056}=84$

iv. $\text{2028}$

Ans: The factorization of $2028$ is as follows:

 $2$ $2028$ $2$ $1014$ $3$ $507$ $13$ $169$ $13$ $13$ $1$

Here, $2028=\underline{2\times 2}\times 3\times \underline{13\times 13}$

We can see that $3$ is not paired

So, we have to multiply $2028$ by $3$ to get a perfect square.

The new number will be $2028\times 3=6084$

$6084=\underline{2\times 2}\times \underline{3\times 3}\times \underline{13\times 13}$ which is a perfect square

$\sqrt{6084}=2\times 3\times 13$

So, $\sqrt{6084}=78$

v. $\text{1458}$

Ans: The factorization of $1458$ is as follows:

 $2$ $1458$ $3$ $729$ $3$ $243$ $3$ $81$ $3$ $27$ $3$ $9$ $3$ $3$ $1$

Here, $1458=2\times \underline{3\times 3}\times \underline{3\times 3}\times \underline{3\times 3}$

We can see that $2$ is not paired

So, we have to multiply $1458$ by $2$ to get a perfect square.

The new number will be $1458\times 2=2916$

$2916=\underline{2\times 2}\times \underline{3\times 3}\times \underline{3\times 3}\times \underline{3\times 3}$ which is a perfect square

$\sqrt{2916}=2\times 3\times 3\times 3$

So, $\sqrt{2916}=54$

vi. $\text{768}$

Ans: The factorization of $768$ is as follows:

 $2$ $768$ $2$ $384$ $2$ $192$ $2$ $96$ $2$ $48$ $2$ $24$ $2$ $12$ $2$ $6$ $3$ $3$ $1$

Here, $768=\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times 3$

We can see that $3$ is not paired

So, we have to multiply $768$ by $3$ to get a perfect square.

The new number will be $768\times 3=2304$

$2304=\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{3\times 3}$ which is a perfect square

$\sqrt{2304}=2\times 2\times 2\times 2\times 3$

So, $\sqrt{2304}=48$

6. For each of the following numbers, find the smallest whole number by   which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained.

i. $\text{252}$

Ans: The factorization of $252$ is as follows:

 $2$ $252$ $2$ $126$ $3$ $63$ $3$ $21$ $7$ $7$ $1$

Here, $252=\underline{2\times 2}\times \underline{3\times 3}\times 7$

We can see that $7$ is not paired

So, we have to divide $252$ by $7$ to get a perfect square.

The new number will be $252\div 7=36$

$36=\underline{2\times 2}\times \underline{3\times 3}$ which is a perfect square

$\sqrt{36}=2\times 3$

So, $\sqrt{36}=6$

ii. $\text{2925}$

Ans: The factorization of $2925$ is as follows:

 $3$ $2925$ $3$ $975$ $5$ $325$ $5$ $65$ $13$ $13$ $1$

Here, $2925=\underline{3\times 3}\times \underline{5\times 5}\times 13$

We can see that $13$ is not paired

So, we have to divide $2925$ by $13$ to get a perfect square.

The new number will be $2925\div 13=225$

$225=\underline{3\times 3}\times \underline{5\times 5}$ which is a perfect square

$\sqrt{225}=3\times 5$

So, $\sqrt{225}=15$

iii. $\text{396}$

Ans: The factorization of $396$ is as follows:

 $2$ $396$ $2$ $198$ $3$ $99$ $3$ $33$ $11$ $11$ $1$

Here, $396=\underline{2\times 2}\times \underline{3\times 3}\times 11$

We can see that $11$ is not paired

So, we have to divide $396$ by $11$ to get a perfect square.

The new number will be $396\div 11=36$

$36=\underline{2\times 2}\times \underline{3\times 3}$ which is a perfect square

$\sqrt{36}=2\times 3$

So, $\sqrt{36}=6$

iv. $\text{2645}$

Ans: The factorization of $2645$ is as follows:

 $5$ $2645$ $23$ $529$ $23$ $23$ $1$

Here, $2645=5\times \underline{23\times 23}$

We can see that $5$ is not paired

So, we have to divide $2645$ by $5$ to get a perfect square.

The new number will be $2645\div 5=529$

$529=\underline{23\times 23}$ which is a perfect square

So, $\sqrt{529}=23$

v. $\text{2800}$

Ans: The factorization of $2800$ is as follows:

 $2$ $2800$ $2$ $1400$ $2$ $700$ $2$ $350$ $5$ $175$ $5$ $35$ $7$ $7$ $1$

Here, $2800=\underline{2\times 2}\times \underline{2\times 2}\times \underline{5\times 5}\times 7$

We can see that $7$ is not paired

So, we have to divide $2800$ by $7$ to get a perfect square.

The new number will be $2800\div 7=400$

$400=\underline{2\times 2}\times \underline{2\times 2}\times \underline{5\times 5}$ which is a perfect square

$\sqrt{400}=2\times 2\times 5$

So, $\sqrt{400}=20$

vi. $\text{1620}$

Ans: The factorization of $1620$ is as follows:

 $2$ $1620$ $2$ $810$ $3$ $405$ $3$ $135$ $3$ $45$ $3$ $15$ $5$ $5$ $1$

Here, $1620=\underline{2\times 2}\times \underline{3\times 3}\times \underline{3\times 3}\times 5$

We can see that $5$ is not paired

So, we have to divide $1620$ by $5$ to get a perfect square.

The new number will be $1620\div 5=324$

$324=\underline{2\times 2}\times \underline{3\times 3}\times \underline{3\times 3}$ which is a perfect square

$\sqrt{324}=2\times 3\times 3$

So, $\sqrt{324}=18$

7. The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Ans: According to the question, each student donated as many rupees as the number of students in the class.

We can find the number of students in the class by doing the square root of the total amount donated by the students of Class VIII.

The total amount donated by students is Rs. $2401$

Then, the number of students in the class will be $\sqrt{2401}$

$\sqrt{2401}=\sqrt{\underline{7\times 7}\times \underline{7\times 7}}$

$=7\times 7$

$=49$

Thus, there are total $49$ students in the class.

8. Around 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Ans: According to the question, the plants are being planted in a garden in such a way that each row contains as many plants as the number of rows.

So, the number of rows will be equal to the number of plants in each row.

Hence,

The number of rows $\times$ Number of plants in each row $=$Total number of plants

The number of rows $\times$ Number of plants in each row $=$ $2025$

The number of rows $\times$ The number of rows $=$ $2025$

The number of rows $=$$\sqrt{2025} \sqrt{2025}=\sqrt{\underline{5\times 5}\times \underline{3\times 3}\times \underline{3\times 3}} =5\times 3\times 3 =45 Thus, the number of rows =45 and the number of plants in each row =45. 9. Find the smallest square number that is divisible by each of the numbers \text{4,9} and \text{10}. Ans: We know that the number that is perfectly divisible by each one of 4,9 and 10 is their L.C.M So, taking the L.C.M of these numbers  2 4,9,10 2 2,9,5 3 1,9,5 3 1,3,5 5 1,1,5 1,1,1 L.C.M=2\times 2\times 3\times 3\times 5 =180 It can be clearly seen that 5 cannot be paired. Therefore, we have to multiply 180 by 5 in order to get a perfect square. Thus, the smallest square number divisible by 4,9 and 10$$=180\times 5=900$

10. Find the smallest square number that is divisible by each of the numbers $\text{8,15}$ and $\text{20}$.

Ans: We know that the number that is perfectly divisible by each one of $8,15$ and $20$ is their L.C.M

So, taking the L.C.M of these numbers

 $2$ $8,15,20$ $2$ $4,15,10$ $2$ $2,15,5$ $3$ $1,15,5$ $5$ $1,5,5$ $1,1,1$

L.C.M$=2\times 2\times 2\times 3\times 5$

$=120$

It can be clearly seen that the prime factors $2$, $3$ and $5$ cannot be paired.

Therefore, we have to multiply $120$ by $2$, $3$ and $5$ in order to get a perfect square.

Thus, the smallest square number divisible by $8, 15$ and $20$ is $120\times 2\times 3\times 5 = 3600$

## What do you learn from Exercise 6.3 Class 8 Maths?

CBSE Class 8 Maths introduces students to squares and square roots in the 6th lesson. In this chapter students get to learn everything about squaring a number, how to derive the square root value of a number, perfect squares, what are perfect squares, properties of square numbers and so on. To get a good grasp over the lesson students may proceed to complete the NCERT Maths Class 8, ex. 6.3 exercises. If you have completed the previous chapter on exponents, then it may not be difficult to understand the problems in exercise 6.3 Class 8 NCERT.

Squares and square roots are one of the most important lessons in Class 8 Mathematics because the chapter not only contributes to advanced Mathematics that you shall study in the future but other Science subjects as well. Squares and square roots are one of the few Mathematical formulae that are applied in algebraic, geometric and trigonometric problems too. Ex 6.3 Class 8 Maths covers some of the most important patterns in square and square root problems. This section covers common and uncommon problems related to the sub-sections and theorems mentioned above.

For instance, a problem from section 6.3 may ask you to find out which among a group of numbers is a perfect square. The NCERT exercise book contains ten sums on the subject, under section 6.3. Students who wish to score well in their CBSE Class 8 Maths paper and wish to score well must try to solve the NCERT exercise on their own and revise it several times.

In the event you are unable to do so on your own, then do not fret, Vedantu is there to help you. Vedantu’s PDF solution guide to NCERT Class 8 Maths, Chapter 6, ex. 6.3 provides accurate, and simplified, step-by-step solutions that can aid in your understanding of Squares and Square Roots. All you need to do is visit Vedantu’s site and download it.

The syllabus is a long-winded one, with numerous important chapters that are highly anticipated in the CBSE test papers. Chapter 6.3, Square and Square Roots happen to be one of the most critically important chapters in the Class 8 Maths syllabus. The chapter presents a long list of problems that form a good percentage of the question paper. So, provided you study the chapter well, square roots can account for a lot of your marks. If you want to get better at solving square root problems, you can always resort to solving the NCERT exercises; and, if the NCERT exercises seem daunting, then you can always count on Vedantu for NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3.

### Vedantu’s PDF Solutions of Class 8 Maths Chapter 6 Exercise 6.3

Vedantu’s NCERT Solution guide can benefit you like it has done for countless students in the past, and continues to do so regularly. Vedantu’s NCERT Solutions for the Class 8, 6th chapter, exercise 6.3 has detailed step-by-step answers that appeal to your understanding of the lesson in a broader, simplified sense. As CBSE students must be aware, their exam papers are modeled quite similarly to the NCERT question-answer model; practicing the sums from the NCERT exercise with the help of the solution and then on your own can make a substantial difference in your understanding of the subject.

If you wish to clear all of your doubts associated with Squares and Square Roots, class 8 Maths Exercise 6.3 solutions you have to study the Vedantu solution guide properly. Every solution is given outlines how numerical problems of different patterns can be tackled and simplified for the deduction. If you are not convinced how much of a difference the solution guide may make, simply attempt the previous ten years’ questions after you are done consulting the steps illustrated in the solution guide. The results shall manifest themselves and help you appear for your CBSE Class 8 Maths paper more confidently.

### Vedantu NCERT Maths Class 8 Chapter 6 Exercise 6.3 Solutions makes exam preparations easier

• Vedantu is a trusted name in the realm of Indian school education. Vedantu’s There are multiple reasons as to why CBSE students can always rely on Vedantu for assistance related to academics.

• Vedantu’s in-house tutors are among some of the most experienced minds in their respective subjects. They have years of experience in their field of study and are quite familiar with the CBSE pattern of questions.

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• The NCERT squares and square roots class 8 exercise 6.3 are provided following the step-marking policies of the CBSE. The numerical problems are solved following the easiest of techniques that students can recall easily.

### NCERT Solution Class 8 Maths Chapter 6 Other Exercises

 Chapter 6 Squares and Square Roots Exercises in PDF Format Exercise 6.1 9 Question and Solutions Exercise 6.2 2 Questions and Solutions Exercise 6.4 9 Questions and Solutions

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## FAQs on NCERT Solutions for Class 8 Maths Chapter 6: Squares and Square Roots - Exercise 6.3

1. How can we Find square roots Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.3) Exercise 6.3?

The square root of a number is the factor that results from multiplying the original number by itself. If "x" equals the square root of "y," then X × X = Y.It is easy to determine the square root of a perfect square integer. Positive integers that may be expressed as the sum of two numbers are called "perfect squares." Positive numbers that can be expressed as the product of a single number are called perfect squares. In layman's terms, perfect squares are those numbers that can be written as the value of any number's power 2.

2. What is the use of repeated subtraction to calculate the square root  Class 8 Maths Chapter 6 Squares and Square?

In the repeated subtraction method, the square root of the number is calculated by subtracting each succeeding odd integer until the result equals zero. The number of times we subtract will be equal to the square root of the supplied number. This method can only be applied to perfect square numbers.

3. How Using prime factorization, we can find the square root in Class 8 Maths Chapter 6 Squares and Square?

The following steps must be taken to use the prime factorization method to determine the square root of a given number:

1. Primarily, determine the prime factors of the given number.

2. Next, group related factors into pairs by ensuring that each pair's two components are equal.

3. Select one element from each pair.

4. Next, calculate the product of the factors you got by taking one from each pair of factors.

5. The square root of the specified number is equal to the product value.

4. How does Vedantu NCERT Maths Class 8 Chapter 6 Exercise 6.3 Solutions make exam preparations easier?

Here are some of the ways that Vedantu NCERT Maths Class 8 Chapter 6 Exercise 6.3 Solutions make exam preparation easier:

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5. Why are Class 8 Maths Chapter 6 Squares and Square Roots so important?

It is important in the formula for the roots of a quadratic equation. Based on square roots, quadratic fields and rings of quadratic integers are important in algebra and have been used in geometry. Square roots are frequently used in foreign mathematical and scientific formulas. These concepts simplify and streamline problem-solving, which is especially useful when performing extensive and time-consuming calculations.