Read the RD Sharma Solutions for Class 8 Maths Chapter 4 – Cubes and Cube Roots, designed to help students master the topic and score high marks in their exams. These RD SHarma solutions offer detailed explanations and step-by-step methods, making it easier for students to understand key concepts.
The solutions are prepared by subject experts and follow the latest RD Sharma Class 8 textbook patterns. By practicing these solved exercises, students can strengthen their basics and boost their confidence for the annual exams.
This chapter includes five exercises covering various important topics. The RD Sharma Class 8 Maths Solutions provided here give complete answers to all exercise questions. Here’s what you will learn in this chapter:
- Cube of a number – Understanding perfect cubes using natural numbers.
- Finding the cube of a two-digit number using the column method.
- Cubes of negative integers and how they behave.
- Cubes of rational numbers explained simply.
- Cube root of a natural number.
- Cube root of a negative perfect cube.
- Cube root of a product of integers.
- How to use cube root tables to easily find cube roots.
These solutions make learning Cubes and Cube Roots simple and effective. Practise regularly to score well and understand Maths concepts clearly.
Download PDF of RD Sharma Class 8 Maths Solutions Chapter 4 Cubes and Cube Roots
Get complete RD Sharma Solutions for Class 8 Maths Chapter 4 Cubes and Cube Roots right here. These solutions provide step-by-step explanations for every question from chapter 4 based on the latest RD Sharma textbook edition.
You can also download the PDF of RD Sharma Class 8 Chapter 4 Solutions for quick and easy access anytime. If you are facing any difficulty with Chapter 4, these detailed solutions will help you clear your doubts and improve your understanding of cubes and cube roots. Regular practice with these solutions can help you score better marks in your Maths exam.
Access Answers to RD Sharma Solutions for Class 8 Maths Chapter 4 Cubes and Cube Roots
Q. Write the cubes of all natural numbers between 1 and 10 and verify the following statements:
(i) Cubes of all odd natural numbers are odd.
(ii) Cubes of all even natural numbers are even.
Solution:
(i) Cubes of all odd natural numbers are odd
Odd numbers between 1 and 10 are:
1, 3, 5, 7, 9
Cube of 1 = 1 (odd)
Cube of 3 = 27 (odd)
Cube of 5 = 125 (odd)
Cube of 7 = 343 (odd)
Cube of 9 = 729 (odd)
The cube of every odd number is odd.
Q. Find the cubes of the following numbers:
(i) 7
(ii) 12
(iii) 16
(iv) 21
(v) 40
(vi) 55
(vii) 100
(viii) 302
(ix) 301
Solution: (i) 7³
Multiply 7 by itself three times:
7 × 7 = 49
49 × 7 = 343
Answer:7³ = 343
(ii) 12³ 12 × 12 = 144
144 × 12 = 1728
Answer:12³ = 1728
(iii) 16³ 16 × 16 = 256
256 × 16 = 4096
Answer:16³ = 4096
(iv) 21³
21 × 21 = 441
441 × 21 = 9261
Answer:21³ = 9261
(v) 40³
40 × 40 = 1600
1600 × 40 = 64000
Answer:40³ = 64000
(vi) 55³
55 × 55 = 3025
3025 × 55 = 166375
Answer:55³ = 166375
(vii) 100³
100 × 100 = 10000
10000 × 100 = 1000000
Answer:100³ = 1000000
(viii) 302³
302 × 302 = 91204
91204 × 302 = 27543608
Answer:302³ = 27543608
(ix) 301³
301 × 301 = 90601
90601 × 301 = 27270901
Answer:301³ = 27270901
Q. Write the cubes of 5 natural numbers, which are multiples of 3 and verify the followings:
The cube of a natural number which is a multiple of 3 is a multiple of 27
Solution:
Let's take five natural numbers that are multiples of 3:
3, 6, 9, 12, and 15.
Step 1: Find the cubes of these numbers:
- The cube of 3 is 3 × 3 × 3 = 27
- The cube of 6 is 6 × 6 × 6 = 216
- The cube of 9 is 9 × 9 × 9 = 729
- The cube of 12 is 12 × 12 × 12 = 1728
- The cube of 15 is 15 × 15 × 15 = 3375
Step 2: Check if these cubes are divisible by 27
Now, we check if all these cubes can be divided by 27 without any remainder.
- 27 ÷ 27 = 1, so 27 is divisible by 27.
- 216 ÷ 27 = 8, so 216 is divisible by 27.
- 729 ÷ 27 = 27, so 729 is divisible by 27.
- 1728 ÷ 27 = 64, so 1728 is divisible by 27.
- 3375 ÷ 27 = 125, so 3375 is divisible by 27.
All the cubes are divisible by 27.
Q. Write the cubes 5 natural numbers of the form 3n+2(i.e.5,8,11….) and verify the following:
The cube of a natural number of the form 3n+2 is a natural number of the same form i.e. when it is divided by 3, the remainder is 2
Solution:
We need to take five natural numbers of the form 3n + 2, which means numbers that give remainder 2 when divided by 3.
These numbers are:
5, 8, 11, 14, 17
Step 1: Find the cubes of these numbers
- 5³ = 5 × 5 × 5 = 125
- 8³ = 8 × 8 × 8 = 512
- 11³ = 11 × 11 × 11 = 1331
- 14³ = 14 × 14 × 14 = 2744
- 17³ = 17 × 17 × 17 = 4913
Step 2: Check what remainder we get when these cubes are divided by 3
- 125 ÷ 3 = 41 remainder 2
- 512 ÷ 3 = 170 remainder 2
- 1331 ÷ 3 = 443 remainder 2
- 2744 ÷ 3 = 914 remainder 2
- 4913 ÷ 3 = 1637 remainder 2
Final Answer:
The cube of any natural number of the form 3n + 2 will also give remainder 2 when divided by 3.
Q. Which of the following are perfect cubes?
(i) 64
(ii) 216
(iii) 243
(iv) 1000
(v) 1728
(vi) 3087
(vii) 4608
(viii) 106480
(ix) 166375
(x) 456533
Solution:
A perfect cube is a number that can be written as the cube of a whole number (natural number).
Let’s check each number one by one.
Step 1: Check each number
(i) 64
64 = 4³ - Perfect Cube
(ii) 216
216 = 6³ - Perfect Cube
(iii) 243
243 is not a perfect cube (it is 3⁵).
(iv) 1000
1000 = 10³ - Perfect Cube
(v) 1728
1728 = 12³ - Perfect Cube
(vi) 3087
3087 is not a perfect cube (it doesn't give a whole number cube root).
(vii) 4608
4608 is not a perfect cube.
(viii) 106480
106480 is not a perfect cube.
(ix) 166375
166375 = 55³ → Perfect Cube
(x) 456533
456533 is not a perfect cube.
Final Answer:
Perfect Cubes are: 64, 216, 1000, 1728, 166375
Not Perfect Cubes: 243, 3087, 4608, 106480, 456533
How to Download Important RD Sharma Solutions Class 8 Maths Chapter 4 Cubes and Cube Roots Free PDF
RD Sharma Solutions for Class 8 Maths Chapter 4 Cubes and Cube Roots are available for free on Home-Tution website. You can easily download free PDF samples of these solutions anytime. These RD Sharma Solutions help students score better marks by explaining each topic in a simple way. Since Class 8 is very important,Home-Tution expert teachers have solved all the problems from the RD Sharma book in easy, step-by-step methods. This helps students understand the concepts clearly. Chapter 4, Cubes and Cube Roots, has five exercises. The RD Sharma Class 8 Solutions on this page give answers to all the questions in each exercise to make learning easier.
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Frequently Asked Questions
Ans. This chapter includes perfect cubes, cube roots of natural and negative numbers, cubes of rational numbers, and finding cube roots via methods like prime factorization and cube root tables
Ans. You can freely download PDFs of all five exercises (4.1–4.5) from educational platforms like Home-Tution.
Ans. With step-by-step explanations, these solutions clarify concepts clearly and help students avoid common mistakes and strengthen problem-solving skills.
Ans. Yes, several sites offer extra worksheets, important questions, and exercise boosters for more practice alongside RD Sharma Chapter 4.