NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots

Q: What are the important topics of chapter Cubes and Cube Roots ?

Finding cubes and cubes roots for numbers containing up to 3 digits, estimating square roots and cube roots are two important topics of this chapter.

Q: How does the NCERT solutions are helpful ?

NCERT solutions not only helpful for the students if they stuck while solving NCERT problems but also they will get conceptual clarity as these solutions are provided in a very detailed manner.

Q: Does CBSE provide NCERT solution for class 8 ?

No, CBSE doesn't provide NCERT solutions for any class and subject.

Q: Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

Q: Where can I find the complete solutions of NCERT for class 8 maths ?

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

Q: How many chapters are there in the CBSE class 8 maths ?

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots

Edited By Ramraj Saini | Updated on Mar 01, 2024 06:26 PM IST

Cubes and Cube Roots Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at craeers360 keeping the latest syllabus and pattern of CBSE 2023-23. In this article, you will get NCERT solutions for Class 8 Maths chapter 7 Cubes and Cube Roots. Cube is a well-known shape in geometry that comes with 3- dimensions that have all sides equal but here we will not discuss that cube. In this chapter, you are going to learn how cubes and cube roots are calculated for a given number.

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This Story also Contains

Cubes and Cube Roots Class 8 Questions And Answers PDF Free Download
Cubes and Cube Roots Class 8 Solutions - Important Formulae
Cubes and Cube Roots Class 8 NCERT Solutions (Intext Questions and Exercise)
Cubes and cube roots class 8 solutions - Topics
NCERT Solutions for Class 8 Maths - Chapter Wise
NCERT Solutions for Class 8 - Subject Wise
NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots - Benefits
Also Check NCERT Books and NCERT Syllabus here

NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots

There are 2 exercises with 7 questions in this chapter. You will get detailed explanations of all these questions in the NCERT solutions for class 8 maths chapter 7 cubes and cube roots. Here you will get the detailed NCERT Solutions for Class 8 by clicking on the link. practice them to command the concepts and score well in the exam.

Cubes and Cube Roots Class 8 Questions And Answers PDF Free Download

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Cubes and Cube Roots Class 8 Solutions - Important Formulae

Cube Root Formula: For any number m, which can be expressed as the product of any number three times, m = n × n × n = n³,

the cube root of m is denoted as: ³√m = n

Methods of Finding Cube Roots:

Prime Factorization Method
Estimation Method

Free download NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots for CBSE Exam.

Cubes and Cube Roots Class 8 NCERT Solutions (Intext Questions and Exercise)

Class 8 maths chapter 7 question answer - Topic 7.2 Cubes

Q(i) Find the one’s digit of the cube of each of the following numbers.

3331

Answer: The detailed solution for the above-mentioned question is as follows,

Since the given number ends with 1, so the one’s digit of the cube of 3331 will be 1.

Q(ii) Find the one’s digit of the cube of each of the following numbers.

8888

Answer: The detailed solution for the above-mentioned question is as follows

Since the given number ends with 8, so the one’s digit of the cube of 8888 will be 2.

Q(iii) Find the one's digit of the cube of each of the following numbers.

149

Answer: The detailed solution for the above-mentioned question is as follows,

Since the given number has 9 at units place, so the one’s digit of the cube of 149 will be 9.

Q(iv) Find the one’s digit of the cube of each of the following numbers.

1005

Answer: The detailed solution for the above-mentioned questions is as follows

Since the given number ends with 5, so one's digit of its cube will also end with 5.

Q(v) Find the one’s digit of the cube of each of the following numbers.

1024

Answer: The solution to the above-mentioned question is as follows,

The given digit is ending with 4. So the one’s digit of the cube of 1024 will be 4.

Q(vi) Find the one’s digit of the cube of each of the following numbers.

Answer: The detailed solution for above-mentioned question is as follows,

The given number is ending with 7, so its cube will end with 3.

Q(vii) Find the one’s digit of the cube of each of the following numbers.

5022

Answer: The detailed solution for the above-mentioned question is as follows,

Since the given number ends with 2, so its cube will end with 8.

Q(viii) Find the one’s digit of the cube of each of the following numbers.

Answer: The detailed solution for the above-mentioned question is as follows,

Since the given number has 3 at units place, so, its cube will end with 7.

Class 8 cubes and cube roots NCERT solutions - Topic 7.2.1 Some Interesting Patterns

Q(a) Express the following numbers as the sum of odd numbers using the above pattern?

$6^{3}$

Answer: The detailed solution for the above mentioned question is as follows,

$6^3 =$ 216 => 31 + 33 + 35 + 37 + 39 + 41

Q(b) Express the following numbers as the sum of odd numbers using the above pattern?

$8^{3}$

Answer: The detailed solution for the above-mentioned question is as follows

$8^3 =$ 512 => 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71

Q(c) Express the following numbers as the sum of odd numbers using the above pattern?

$7^{3}$

Answer: The detailed solution for the above-mentioned question is as follows

7 ³ = 43 + 45 + 47 + 49 + 51 + 53 + 55

Q(i) The detailed solution of the above-written question is as follows,

Using the above pattern

$2^{3}-1^{3}=1+2\times 1\times 3$

$3^{3}-2^{3}=1+3\times2\times 3$

$4^{3}-3^{3}=1+4\times 3\times 3$

find the value of the following

$7^{3}-6^{3}$

Answer: The value of the following question is:

$7^{3}-6^{3} =$ $7^{3}-6^{3} = 1 + 7\times6\times3 = 1 + 126 = 127$

Q(ii) The detailed solution for all the above-written question is as follows

Using the above pattern

$2^{3}-1^{3}=1+2\times 1\times 3$

$3^{3}-2^{3}=1+3\times2\times 3$

$4^{3}-3^{3}=1+4\times 3\times 3$

find the value of the following.

$12^{3}-11^{3}$

Answer: $12^{3}-11^{3} = 1 + 12\times11\times3 = 1 + 396 = 397$

Q(iii). Consider the following pattern.

$2^{3}-1^{3}=1+2\times 1\times 3$

$3^{3}-2^{3}=1+3\times2\times 3$

$4^{3}-3^{3}=1+4\times 3\times 3$

Using the above pattern, find the value of the following.

$20^{3}-19^{3}$

Answer: The detailed solution for the above-written question is mentioned below,

$20^{3}-19^{3} = 1 + 20\times19\times3 = 1 + 1140 = 1141$

Q(iv) Consider the following pattern.

$2^{3}-1^{3}=1+2\times 1\times 3$

$3^{3}-2^{3}=1+3\times2\times 3$

$4^{3}-3^{3}=1+4\times 3\times 3$

Using the above pattern , find the value of the following.

$51^{3}-50^{3}$

Answer: The detailed solution for the above written question is mentioned below

$51^{3}-50^{3} = 1 + 51\times50\times3 = 1 + 7650 = 7651$

NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Topic 7.2.1 Subtopic Cubes and Their Prime Factors

Q. Which of the following are perfect cubes?

1. 400

2. 3375

3. 8000

4. 15625

5. 9000

6. 6859

7. 2025

8. 10648

Answer: We will find it by prime factorization whether they make a pair of three prime numbers or not.

(1) $400 = 2\times2\times2\times2\times5\times5$ . So not a perfect cube.

(2) $3375 = 3\times3\times3\times5\times5\times5$ . So it is a perfect cube.

(3) $8000 = 2\times2\times2\times2\times2\times2\times5\times5\times5$ . So it is a perfect cube.

(4) $15625 = 5\times5\times5\times5\times5\times5$ . So it is a perfect cube.

(5) $9000 = 2\times2\times2\times3\times3\times5\times5\times5$ . So it is not a perfect cube.

(6) $6859 = 19\times19\times19$ . So it is a perfect cube.

(7) $2025 = 3\times3\times3\times3\times5\times5$ . So it is not a perfect cube.

(8) $10648 = 2\times2\times2\times11\times11\times11$ . So it is a perfect cube.

NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Topic 7.2.2 Smallest Multiple That is a Perfect Cube

Q. Check which of the following are perfect cubes.

(i) 2700

(ii) 16000

(iii) 64000

(iv) 900

(v) 125000

(vi) 36000

(vii) 21600

(viii) 10,000

(ix) 27000000

(x) 1000.

What pattern do you observe in these perfect cubes?

Answer: The detailed solution for the above-written question is as follows

By prime factorization:

(i) $2700 = 2\times2\times3\times3\times3\times5\times5$ . So it is not a perfect cube.

(ii) $16000 = 2\times2\times2\times2\times2\times2\times2\times5\times5\times5$ . So it is not a perfect cube.

(iii) $64000 = 2\times2\times2\times2\times2\times2\times2\times2\times2\times5\times5\times5= 80\times80\times80$ . So it is a perfect cube.

(iv) $900 = 2\times2\times3\times3\times5\times5$ . So it is not a perfect cube.

(v) $125000 = 2\times2\times2\times5\times5\times5\times5\times5\times5$ . So it is a perfect cube.

(vi) $36000 = 2\times2\times2\times2\times2\times3\times3\times5\times5\times5$ . So it is not a perfect cube.

(vii) $21600 = 2\times2\times2\times2\times2\times3\times3\times3\times5\times5$ . So it is not a perfect cube.

(viii) $10000 = 2\times2\times2\times2\times5\times5\times5\times5$ . So it is not a perfect cube.

(ix) $27000000 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times5\times5\times5\times5\times5\times5$ . So it is a perfect cube.

(x) $1000 = 2\times2\times2\times5\times5\times5$ . So it is a perfect cube.

We observe that the numbers above which are perfect cube have the number of zeros in multiple of 3.

Class 8 maths chapter 7 question answer - Exercise: 7.1

Q.1(i) Which of the following numbers are not perfect cubes?

216

Answer: The detailed solution for the above-written question is as follows

By prime factorization of 216 gives:

$216 = 2\times2\times2\times3\times3\times3$

Since prime numbers are present in pairs of three, so the given number is a perfect cube.

Q.1(ii) Which of the following numbers are not perfect cubes?

128

Answer: We have 128. By prime factorization we get,

$128 = 2\times2\times2\times2\times2\times2\times2$

Since the prime numbers are not in pairs of three, so the given number is not a perfect cube.

Q.1(iii) Which of the following numbers are not perfect cubes?

1000

Answer: The detailed solution for the above written is as follows

By prime factorization of 1000 we get :

$1000 = 2\times2\times2\times5\times5\times5$ .

So the given number is a perfect cube.

Q.1(iv) Which of the following numbers are not perfect cubes?

100

Answer: The detailed solution for the above-written question is as follows

By prime factorization of 100 :

$100 = 2\times2\times5\times5$ .

Since prime numbers are not in pair of three so given number is not a perfect cube.

Q.1(v) Which of the following numbers are not perfect cubes?

46656

Answer: We have 46656, by prime factorisation:

$46656 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times3\times3\times3$ .

Since prime numbers are in group of three. So the given number is a perfect cube.

Q.2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243

(ii) 256

(iii) 72

(iv) 675

(v) 100

Answer: This can be found by knowing about the prime factors of the number.

(i) 243 : $3\times3\times3\times3\times3$ .

So it must be multiplied by 3.

(ii) 256 : $2\times2\times2\times2\times2\times2\times2\times2$

So the given number must be multiplied by 2 to make it a perfect cube.

(iii) 72 : $2\times2\times2\times3\times3$

So 72 must be multiplied by 3 to make it a perfect cube.

(iv) 675 : $3\times3\times3\times5\times5$

So it should be multiplied by 5.

(v) 100 : $2\times2\times5\times5$

So it should be multiplied by 10.

Q.3 Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.

(i) 81

(ii) 128

(iii) 135

(iv) 192

(v) 704

Answer: By prime factorization of given numbers :

(i) 81 : $3\times3\times3\times3$

So given number needs to be divided by 3 to get a perfect cube.

(ii) 128 : $2\times2\times2\times2\times2\times2\times2$ .

So the given number needs to be divided by 2 to get a perfect cube.

(iii) 135 : $3\times3\times3\times5$

So the given number needs to be divided by 5 to get a perfect cube.

(iv) 192 : $2\times2\times2\times2\times2\times2\times3$

So the given number needs to be divided by 3 to get a perfect cube.

(v) 704 : $2\times2\times2\times2\times2\times2\times11$

So the given number needs to be divided by 11 to get a perfect cube.

Q.4 Parikshit makes a cuboid of plasticine of sides $5\: cm,2\; cm,5\; cm$ . How many such cuboids will he need to form a cube?

Answer: Volume of cuboid is $5\times2\times5 = 2\times5\times5$ $cm^3$

To make it a cube need to make this a pefect cube number.

So we need $2\times2\times5$ cuboids

or 20 cuboids.

Q. State true or false:

for any integer $m,m^{2}< m^{3}.$ Why?

Answer: The detailed solution for the above-written question is as follows.

False.

$m^2 < m^3$

or $0 < m^3 - m^2$

or $m^3 - m^2>0$

or $m^2\left ( m-1 \right )>0$

Now put any number less than 1, we see that this relation doesn't hold.

So for m<1 this condition is not true.

Class 8 maths chapter 7 NCERT Solutions - Exercise: 7.2

Q.1(i) Find the cube root of each of the following numbers by prime factorisation method.

Answer: The detailed solution for the above-written question is as follows

Prime factorization of 64 gives :

$64 = 2\times2\times2\times2\times2\times2$

So its cube root is $2\times2$ = 4

Q.1(ii) Find the cube root of each of the following numbers by prime factorisation method.

512

Answer: By prime factorisation of 512 :

$512 = 2\times2\times2\times2\times2\times2\times2\times2\times2$

So its cube root is $2\times2\times2 = 8$

Q.1(iii) Find the cube root of each of the following numbers by prime factorisation method.

10648

Answer: The detailed solution for the above-written question is as follows

Prime factorization of 10648 gives :

$10648 = 2\times2\times2\times11\times11\times11$

So its cube root is 22.

Q.1(iv) Find the cube root of each of the following numbers by prime factorisation method.

27000

Answer: The detailed solution for the above-written question is as follows

By prime factorization method, we get :

$27000 = 2\times2\times2\times3\times3\times3\times5\times5\times5$

So its cube root is 30.

Q.1(v) Find the cube root of each of the following numbers by prime factorisation method.

15625

Answer: The detailed solution for the above-written question is as follows

By prime factorization:

$15625 = 5\times5\times5\times5\times5\times5$

So its cube root is 25.

Q.1(vi) Find the cube root of each of the following numbers by prime factorisation method.

13824

Answer: The detailed solution for the above-written question is as follows

By prime factorization:

$13824 = 2\times2\times2\times2\times2\times2\times2\times2\times2\times3\times3\times3$

So its cube root is 24.

Q.1(vii) Find the cube root of each of the following numbers by prime factorisation method.

110592

Answer: The detailed solution for the above-written question is as follows

By prime factorization:

$110592 = 2\times2\times2\times2\times2\times2\times2\times2\times2\times2\times2\times2\times3\times3\times3$

So its cube root is $2\times2\times2\times2\times3$ = 48.

Q.1(viii) Find the cube root of each of the following numbers by prime factorisation method.

46656

Answer: The detailed solution for the above-written question is as follows

By prime factorization, we get :

$46656 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times3\times3\times3$

So its cube root is $2\times2\times3\times3$ = 36.

Q.1(ix) Find the cube root of each of the following numbers by prime factorisation method.

175616

Answer: The detailed solution for the above-written question is as follows

By prime factorization we get :

$175616 = 2\times2\times2\times2\times2\times2\times2\times2\times2\times7\times7\times7$

So its cube root is $2\times2\times2\times7$ = 56.

Q.1(x) Find the cube root of each of the following numbers by prime factorisation method.

91125

Answer: The detailed solution for the above-written question is as follows

By prime factorization, we get :

$91125 = 3\times3\times3\times3\times3\times3\times5\times5\times5$

So its cube root is $3\times3\times5$ = 45.

Q2. State true or false.

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeros.

(iii) If square of a number ends with 5, then its cube ends with 25.

(iv) There is no perfect cube which ends with 8

(v) The cube of a two digit number may be a three digit number.

(vi) The cube of a two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.

Answer: (i) False. Cube of an odd number can never be even.

(ii) True. Perfect cube number ends with zeros multiple of three.

(iii) False. We can say only about units place.

(iv) False. Cube of numbers which ends with 2 end with 8.

(v) False. Can never be.

(vi) False. Can never be. It can be proved by taking examples.

(vii) True. e.g. 1,2

Q.3 You are told that 1,331 is a perfect cube. Can you guess without factorisation what
is its cube root? Similarly, guess the cube roots of

4913,

12167,

32768.

Answer: We have 1331.

Divide number in two parts: The first part is 1 and second is 331.

Since the given number is ending with 1 so the last digit of cube root will be 1.

In the first part, we have 1.

So $1^3 = 1$

By estimation, the cube root of 1331 is 11.

Similarly for all other parts.

4913:- First part is 4 and the second part is 913.

The number is ending with 3 so its cube root will have 7 at units place.

In the first part, the nearest cube root is 1.

So the cube root of 4913 is 17.

12167:- First part is 12 and the second part is 167.

The number is ending with 7 so its cube root will have 3 at units place.

In the first part, the nearest cube root is 2.

So the cube root of 12167 is 23.

32768:- First part is 32 and the second part is 768.

The number is ending with 8, so its cube root will have 2 at units place.

In the first part, the nearest cube root is 3.

So the cube root of 32768 is 32.

Cubes and cube roots class 8 solutions - Topics

Cubes
Cube Roots

NCERT Solutions for Class 8 Maths - Chapter Wise

Chapter -1	Rational Numbers
Chapter -2	Linear Equations in One Variable
Chapter-3	Understanding Quadrilaterals
Chapter-4	Practical Geometry
Chapter-5	Data Handling
Chapter-6	Squares and Square Roots
Chapter-7	Cubes and Cube Roots
Chapter-8	Comparing Quantities
Chapter-9	Algebraic Expressions and Identities
Chapter-10	Visualizing Solid Shapes
Chapter-11	Mensuration
Chapter-12	Exponents and Powers
Chapter-13	Direct and Inverse Proportions
Chapter-14	Factorization
Chapter-15	Introduction to Graphs
Chapter-16	Playing with Numbers

NCERT Solutions for Class 8 - Subject Wise

NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots - Benefits

These solutions for ch 7 maths class 8 are prepared in a very simple language which can be understood very easily
You will learn some short tricks, so you can solve the problem in minimal time.
You should try to solve every problem of the textbook including examples and practice questions given after every topic. If are having difficulty while solving, these solutions are hare to help you.
NCERT solutions for maths chapter 7 class 8, you will get solutions to practice question which is given after every topic also.
These class 8 maths ch 7 question answer will help you with homework as well.

Also Check NCERT Books and NCERT Syllabus here

Frequently Asked Questions (FAQs)

1. What are the important topics of chapter Cubes and Cube Roots ?

Finding cubes and cubes roots for numbers containing up to 3 digits, estimating square roots and cube roots are two important topics of this chapter.

2. How does the NCERT solutions are helpful ?

NCERT solutions not only helpful for the students if they stuck while solving NCERT problems but also they will get conceptual clarity as these solutions are provided in a very detailed manner.

3. Does CBSE provide NCERT solution for class 8 ?

No, CBSE doesn't provide NCERT solutions for any class and subject.

4. Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

5. Where can I find the complete solutions of NCERT for class 8 maths ?

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

6. How many chapters are there in the CBSE class 8 maths ?

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

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NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots

Cubes and Cube Roots Class 8 Questions And Answers PDF Free Download

Cubes and Cube Roots Class 8 Solutions - Important Formulae

Cubes and Cube Roots Class 8 NCERT Solutions (Intext Questions and Exercise)

Answer: The detailed solution for the above-mentioned question is as follows,

Answer: The detailed solution for the above-mentioned question is as follows

Q(iii) Find the one's digit of the cube of each of the following numbers.

Answer: The detailed solution for the above-mentioned question is as follows,

Answer: The detailed solution for the above-mentioned questions is as follows

Answer: The solution to the above-mentioned question is as follows,

Answer: The detailed solution for above-mentioned question is as follows,

Answer: The detailed solution for the above-mentioned question is as follows,

Answer: The detailed solution for the above-mentioned question is as follows,

Answer: The detailed solution for the above mentioned question is as follows,

Answer: The detailed solution for the above-mentioned question is as follows

Answer: The detailed solution for the above-mentioned question is as follows

Answer: The value of the following question is:

Q(ii) The detailed solution for all the above-written question is as follows

Answer: $12^{3}-11^{3} = 1 + 12\times11\times3 = 1 + 396 = 397$