Students can refer and download the RS Aggarwal Solutions for the Exercise 3B of Class 8 Maths Chapter 3, Squares and Square Roots from the link available here. At BYJUâ€™S, we have a set of expert faculties trying their best to provide exercise-wise solutions to students according to their level of understanding. This exercise can be used as a model of reference by the students to improve their conceptual knowledge and understand the different ways used to solve the problems. Exercise 3B of class 8 helps students to understand the concepts of perfect square properties as well as the product of two consecutive odd or consecutive even numbers. By practising the RS Aggarwal Solutions for class 8, students will be able to grasp the concepts perfectly. It also helps in boosting their confidence, which plays a crucial role in their examinations.

## Download PDF of RS Aggarwal Solutions for Class 8 Chapter 3 – Squares and Square Roots – Exercise 3B

### Access answers to Maths RS Aggarwal Solutions for Class 8 Chapter 3 – Squares and Square Roots Exercise 3B

**Q1. Give reason to show that none of the numbers given below is a perfect square:**

**(i) 5372**

**(ii) 5963**

**(iii) 8457**

**(iv) 9468**

**(v) 360**

**(vi) 64000**

**(vii) 2500000**

** Solution:**

- Given 5372
By observing the property 1 of perfect square i.e. a number ending in 2 is never a perfect square.

Therefore the given number 5372 is not a perfect square.

- Given 5963
We have the property 1 of perfect square i.e. a number ending in 3 is never a perfect square.

Therefore the given number 5963 is not a perfect square.

- Given 8457
We have the property 1 of perfect square i.e. a number ending in 7 is never a perfect square.

Therefore the given number 8457 is not a perfect square.

- Given 9468
We have the property 1 of perfect square i.e. a number ending in 8 is never a perfect square.

Therefore the given number 9458 is not a perfect square.

- Given 360
We know the property 2 of perfect square i.e. a number ending in an add number of zeros is never a perfect square.

Therefore the given number 360 is not a perfect square.

- Given 64000
We know the property 2 of perfect square i.e. a number ending in an add number of zeros is never a perfect square.

Therefore the given number 64000 is not a perfect square.

- Given 2500000
We know the property 2 of perfect square i.e. a number ending in an add number of zeros is never a perfect square.

Therefore the given number 2500000 is not a perfect square.

**Q2. Which of the following are squares of even numbers?**

**(i) 196**

**(ii) 441**

**(iii) 900**

**(iv) 625**

**(v) 324**

**Solution:**

- Given 196
We know that from the property of perfect square, the square of an even number is always even.

So the given number 196 is even, therefore it is square of even number

- Given 441
We know that from the property of perfect square, the square of an even number is always even.

But the given number 441 is odd, therefore it is not a square of even number

- Given 900
We know that from the property of perfect square, the square of an even number is always even.

So the given number 900 is even, therefore it is square of even number

- Given 625
We know that from the property of perfect square, the square of an even number is always even.

But the given number 625 is odd, therefore it is not a square of even number

- Given 324
We know that from the property of perfect square, the square of an even number is always even.

So the given number 324 is even, therefore it is square of even number

**Q3. Which of the following are squares of add numbers?**

**(i) 484**

**(ii) 961**

**(iii) 7396**

**(iv) 8649**

**(v) 4225**

**Solution:**

- Given 484
According to the property of perfect square i.e. the square of a odd number is always odd.

But the given number 484 is not odd

Therefore it is not square of odd number.

- Given 961
According to the property of perfect square i.e. the square of a odd number is always odd.

The given number 961 is odd, therefore it is square of odd number.

- Given 7396
According to the property of perfect square i.e. the square of a odd number is always odd.

But the given number 7396 is not odd

Therefore it is not square of odd number.

- Given 8649
According to the property of perfect square i.e. the square of a odd number is always odd.

The given number 8649 is odd, therefore it is square of odd number.

- Given 4225
According to the property of perfect square i.e. the square of a odd number is always odd.

The given number 4225 is odd, therefore it is square of odd number.

**Q4. Without adding, find the sum:**

**(i) (1+3+5+7+9+11+13)**

**(ii) (1+3+5+7+9+11+13+15+17+19)**

**(iii) (1+3+5+7+9+11+13+15+17+19+21+23)**

**Solution:**

- Given (1+3+5+7+9+11+13)
According to the property of perfect square, for any natural number n, we have sum of first n odd natural numbers=n

^{2}But here n=7

Applying the above law we get

Therefore (1+3+5+7+9+11+13) = 7

^{2 }= 49 - Given (1+3+5+7+9+11+13+15+17+19)
According to the property of perfect square, for any natural number n, we have sum of first n odd natural numbers=n

^{2}But here n=10

Applying the above law we get

Therefore (1+3+5+7+9+11+13+15+17+19) = 10

^{2 }= 100 - Given (1+3+5+7+9+11+13+15+17+19+21+23)
According to the property of perfect square, for any natural number n, we have sum of first n odd natural numbers=n

^{2}But here n=12

Applying the above law we get

Therefore (1+3+5+7+9+11+13+15+17+19+21+23) = 12

^{2 }= 144

**Q5.**

**(i) Express 81 as the sum of 9 odd numbers.**

**(ii) Express 100 as the sum of 10 odd numbers.**

** Solution:**

- Given 81 can be written as 9
^{2}^{2}Expressing 81 as a sum of 9 odd numbers, we get

81= (9)

^{2}Here n=9

By applying the law 81 = (1+3+5+7+9+11+13+15+17)

- Given 100 can be written as 10
^{2}^{2}Expressing 100 as a sum of 10 odd numbers, we get

100 = (10)

^{2}Here n=10

By applying the law 81 = (1+3+5+7+9+11+13+15+17+19)

**Q6. Write a Pythagorean triplet whose smallest member is**

**(i) 6**

**(ii) 14**

**(iii) 16**

**(iv) 20**

** Solution:**

- Given 6 is the smallest number in Pythagorean triplet
But we have for every number m>1, we have (2m, m

^{2}-1, m^{2}+1) as a Pythagorean tripletUsing the above condition we can write as

2m=6

m=6/2=3

Then m

^{2}=9m

^{2 }– 1 = 9 â€“ 1 = 8m

^{2 }+ 1 = 9 + 1 =10Therefore the Pythagorean triplet is = (2m, m

^{2}-1, m^{2}+1) = (6, 8, 10) - Given 14 is the smallest number in Pythagorean triplet
But we have for every number m>1, we have (2m, m

^{2}-1, m^{2}+1) as a Pythagorean tripletUsing the above condition we can write as

2m=14

m= 14/2=7

Then m

^{2 }=49m

^{2 }– 1 = 49 â€“ 1 = 48m

^{2 }+ 1 = 49 + 1 =50Therefore the Pythagorean triplet is = (2m, m

^{2}-1, m^{2}+1) = (14, 48, 50) - Given 16 is the smallest number in Pythagorean triplet
But we have for every number m>1, we have (2m, m

^{2}-1, m^{2}+1) as a Pythagorean tripletUsing the above condition we can write as

2m=16

m= 16/2=8

Then m

^{2 }=64m

^{2 }– 1 = 64 â€“ 1 = 63m

^{2 }+ 1 = 64 + 1 =65Therefore the Pythagorean triplet is = (2m, m

^{2}-1, m^{2}+1) = (16, 63, 65) - Given 20 is the smallest number in Pythagorean triplet
But we have for every number m>1, we have (2m, m

^{2}-1, m^{2}+1) as a Pythagorean tripletUsing the above condition we can write as

2m=20

m= 20/2=10

Then m

^{2 }=100m

^{2 }– 1 = 100 â€“ 1 = 99m

^{2 }+ 1 = 100 + 1 =101Therefore the Pythagorean triplet is = (2m, m

^{2}-1, m^{2}+1) = (20, 99, 101)

**Q7. Evaluate:**

**(i) (38)2 â€“(37)2**

**(ii) (75)2 â€“(74)2**

**(iii) (92)2 â€“(91)2**

**(iv) (105)2 â€“(104)2**

**(v) (141)2 â€“(140)2**

**(vi) (218)2 â€“(217)2**

**Solution:**

- Given (38)
^{2}â€“(37)^{2}According to the property 8 i.e. for every natural number n, we have [(n+1)

^{2}-n^{2}] = [(n+1) + n]Here n=37

By applying the above property we get,

(38)

^{2}â€“ (37)^{2 }= (37+1) + 37 = 38+ 37 = 75 - Given (75)
^{2}â€“(74)^{2}According to the property 8 i.e. for every natural number n, we have [(n+1)

^{2}-n^{2}] = [(n+1) + n]Here n=74

By applying the above property we get,

(75)

^{2}â€“ (74)^{2 }= (74+1) + 74 = 75 + 74 = 149 - Given (92)
^{2}â€“(91)^{2}According to the property 8 i.e. for every natural number n, we have [(n+1)

^{2}-n^{2}] = [(n+1) + n]Here n=91

By applying the above property we get,

(92)

^{2}â€“ (91)^{2 }= (91+1) + 91 = 92 + 91 = 183 - Given (105)
^{2}â€“(104)^{2}^{2}-n^{2}] = [(n+1) + n]Here n=104

By applying the above property we get,

(105)

^{2}â€“ (104)^{2 }= (104+1) + 104 = 105 + 104 = 209 - Given (141)
^{2}â€“(140)^{2}^{2}-n^{2}] = [(n+1) + n]Here n=140

By applying the above property we get,

(141)

^{2}â€“ (140)^{2 }= (140+1) + 140 = 141 + 140 = 281 - Given (218)
^{2}â€“(217)^{2}^{2}-n^{2}] = [(n+1) + n]Here n=217

By applying the above property we get,

= â€“ (217)

^{2 }= (217+1) + 217 = 218 + 217 = 435

**Q8. Using the formula (a + b) ^{2}=(a^{2 }+ 2ab + b^{2}), evaluate:**

**(i) (310)2**

**(ii) (508)2**

**(iii) (630)2**

**Solution: **

- Given (310)
^{2}We have (a + b)

^{2 }= (a^{2 }+ 2ab + b^{2})(310)

^{2 }can be written as 300+10So here a=300 and b=10

Using the formula,

(300 + 10)

^{2 }= (300^{2 }+ 2 X 300 X 10 + 10^{2})On simplifying we get

(300 + 10)

^{2 }= (90000 + 6000 +100)(310)

^{2}=96100 - Given (508)
^{2}We have (a + b)

^{2 }= (a^{2 }+ 2ab + b^{2})(508)

^{2 }can be written as 500+8So here a=500 and b=8

Using the formula,

(500 + 8)

^{2 }= (500^{2 }+ 2 X 500 X 8 + 8^{2})On simplifying we get

(500 + 8)

^{2 }= (250000 + 8000 +64)(508)

^{2 }= 258064 - Given (630)
^{2}We have (a + b)

^{2 }= (a^{2 }+ 2ab + b^{2})(630)

^{2 }can be written as 600+30So here a=300 and b=10

Using the formula,

(600 + 30)

^{2 }= (600^{2 }+ 2 X 600 X 30 + 30^{2})On simplifying we get,

(600 + 30)

^{2 }= (360000 + 3600 +900)(630)

^{2 }= 396900

**Q9. Using the formula (a – b) ^{2}=(a^{2 }– 2ab + b^{2}), evaluate:**

**(i) (196) ^{2}**

**(ii) (689) ^{ 2}**

**(iii) (891) ^{ 2}**

**Solution: **

- Given (196)
^{2}We have (a – b)

^{2 }= (a^{2 }– 2ab + b^{2})(196)

^{2 }can be written as 200-4So here a=200 and b=4

Using the formula,

(200 – 4)

^{2 }= (200^{2 }– 2 X 200 X 4 + 4^{2})On simplifying we get

(200 – 4)

^{2 }= (40000 – 1600 +16)(196)

^{2}=38416 - Given (689)
^{2}We have (a – b)

^{2 }= (a^{2 }– 2ab + b^{2})(689)

^{2 }can be written as 700-11So here a=700 and b=11

Using the formula,

(700 – 11)

^{2 }= (700^{2 }– 2 X 700 X 11 + 11^{2})On simplifying we get

(700 – 11)

^{2 }= (490000 – 15400 +121)(689)

^{2}=474721 - Given (891)
^{2}We have (a – b)

^{2 }= (a^{2 }– 2ab + b^{2})(891)

^{2 }can be written as 900-9So here a=900 and b=9

Using the formula,

(900 – 9)

^{2 }= (900^{2 }– 2 X 900 X 9 + 9^{2})On simplifying we get

(900 – 9)

^{2 }= (810000 – 16200 +81)(891)

^{2}=793881

**Q10. Evaluate: **

**(i) 69 X 71**

**(ii) 94 X 106**

** Solution:**

- Given 69 X 71
We can write 69 as 70-1 and also 71 as 70+1

We know that (a + b) X (a â€“ b) = a

^{2}– b^{2}Here a= 70 and b = 1

Applying the above formula we get

(70 + 1) X (70 â€“ 1) = (70)

^{2 }â€“ (1)^{2}(70 + 1) X (70 â€“ 1) = 4900 â€“ 1= 4899

- Given 94 X 106
We can write 94 as 100-6 and also 106 as 100+6

We know that (a + b) X (a â€“ b) = a

^{2}– b^{2}Here a= 100 and b = 6

Applying the above formula we get

(100 + 6) X (100 â€“ 6) = (100)

^{2 }â€“ (6)^{2}(100 + 6) X (100 â€“ 6) = 10000 â€“ 36= 9964

**Q11. Evaluate: **

**(i) 88 X 92**

**(ii) 78 X 82**

** Solution:**

- Given 88 X 92
We can write 88 as 90-2 and also 92 as 90+2

We know that (a + b) Ã— (a â€“ b) = a

^{2}– b^{2}Here a= 90 and b = 2

Applying the above formula we get

(90 + 2) X (90 â€“ 2) = (90)

^{2 }â€“ (2)^{2}(90 + 2) X (90 â€“ 2) = 8100 â€“ 4= 8096

- Given 78 X 82
We can write 78 as 80-2 and also 82 as 80+2

We know that (a + b) X (a â€“ b) = a

^{2}– b^{2}Here a= 80 and b = 2

Applying the above formula we get

(80 + 2) X (80 â€“ 2) = (80)

^{2 }â€“ (2)^{2}(80 + 2) X (80 â€“ 2) = 6400 â€“ 4= 6396

**Q12. Fill in the blanks:**

**(i) The square of an even number isâ€¦â€¦â€¦.**

**(ii) The square of an odd number isâ€¦â€¦â€¦â€¦**

**(iii) The square of a proper fraction isâ€¦â€¦â€¦. than the given fraction.**

**(iv) n2= the sum of first n â€¦â€¦â€¦ natural numbers.**

**Solution:**

- Even
**Explanation:**According to the property of perfect square i.e. the square of an

Even number is always even.

- Odd
**Explanation:**According to the property of perfect square i.e. the square of an odd number is always odd.

- Smaller
**Explanation:**According to the property of perfect square i.e. the square of a proper fraction is smaller than the fraction.

- Odd
**Explanation:**According to the property of perfect square i.e. for ever natural number n, we have sum of first n odd natural numbers = n

^{2}

**Q13. Write (T) for true and (F) for false for each of the statements given below:**

**(i) The number of digits in a perfect square is even.**

**(ii) The square of a prime number is prime.**

**(iii) The sum of two perfect squares is a perfect squares.**

**(iv) The difference of two perfect squares is a perfect square.**

**(v) The product of two perfect squares is a perfect squares.**

**Solution:**False

**Explanation:**Because the number of digits present in perfect square also be odd.

**Solution:**False

**Explanation:**A prime number is one that is not divisible by any other, except by 1 and itself. So square of a prime number is not always prime.

**Solution:**False

**Explanation:**The sum of two perfect square can be any number.

**Solution:**False

**Explanation:**The difference of two perfect square can be any number.

**Solution:**True

**Explanation:**According to the properties of perfect square we have,

The product of two perfect squares is a perfect square.

### Access other exercises of RS Aggarwal Solutions for Class 8 Chapter 3 – Squares and Square Roots

Exercise 3A Solutions 6 questions

Exercise 3C Solutions 8 questions

Exercise 3D Solutions 18 questions

Exercise 3E Solutions 19 questions

Exercise 3F Solutions 12 questions

Exercise 3G Solutions 10 questions

Exercise 3H Solutions 19 questions

## RS Aggarwal Solutions for Class 8 Maths Chapter 3 – Squares and Square Roots Exercise 3B

deals with the basic concepts related to properties of a perfect square. We can say that this exercise mainly deals with the properties of perfect squares such as Pythagorean Triplets, the sum of first â€˜nâ€™ odd natural numbers, etc. that the students have learned in this chapter. This exercise contains 13 main questions and all questions are based on properties of perfect squares. Some of the topics focused prior to exercise 3B include the following.

Properties of a perfect square

Pythagorean Triplets

Product of two consecutive odd numbers

Product of two consecutive even numbers