NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.1 Cubes and Cube Roots - PDF Download

NCERT solutions for class 8 maths chapter 6 ex 6.1 Cube and Cube Roots is about cubes of numbers and their relationship with the original numbers and the cubes of consecutive numbers. The students will learn about the odd and even properties of a cube, how to figure out the cube root, and the prime factor of a cube. 

Class 8 maths chapter 6 exercise 6.1 NCERT solutions questions need to find the perfect cubes and also help the students understand how to multiply a number to get to the nearest perfect cube. The prime factors of any cube appear three times in the factors, so this property can be used to tell if a number is a cube or not.

Ex 6.1 class 8 maths solutions consists of 4 questions with its sub-parts. Class 8 maths ex 6.1 NCERT solutions are explained by our subject experts of maths for students to prepare well for the exam. These solutions are available in free PDF format and in accordance with the guidance of CBSE. Students can also download NCERT solutions for class 8 maths PDF to make their preparation easier.

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Topics Covered in Exercise 6.1 Class 8 Mathematics Questions

Ex 6.1 class 8 maths chapter 6 NCERT solutions is based on the concepts of finding the perfect cube and cube roots which you can check below.

1. Cubes - A cube is a three-dimensional shape with all of its sides equal.

If a cube has all sides equal to 1 cm, how many sides of 2 cm are needed to form a new cube?

8 such cubes are required, and what if we need to make a cube of side 3 cm with the cubes of side 1 cm? The numbers 1, 8, 27 ...etc can be shown below in the cube.

These are called perfect cubes or cube numbers. This means that we have the cube numbers by multiplying the number three times by itself.

• Some interesting patterns

1. Adding consecutive odd numbers - This proves that if you add the consecutive odd numbers, then you get a cube of the next number.
2. Cubes and their prime factors - The process of prime factorization is to find the prime factors of a number and then pairing them in a group of three. If you have all of the prime factors in a pair of three, then you have a perfect cube.

• Smallest multiple that is a perfect cube

Now that we know that the group of 3 prime factors creates a number perfect cube. We need to multiply it by the smallest multiple of that number to make it a perfect cube number.

Tips for Solving Exercise 6.1 Class 8 Chapter 6 Cubes and Cube Roots

NCERT solutions class 8 maths chapter 6 ex 6.1 comprised questions based on cubes and its properties. To solve these questions of ex 6.1 you need to follow some useful tips. 

1. To solve exercise 6.1 questions, students must understand the concepts of cubes and its properties like adding consecutive odd numbers, cubes and their prime factors and multiples that are perfect cubes.
2. While performing the ex 6.1 questions in NCERT solutions class 8 maths, you should be very curious about how the numbers, and their cubes, relate to each other and to the other numbers surrounding them.
3. Students also need to solve examples given in chapter 6 ex 6.1 before solving the exercise questions.

Importance of Solving Ex 6.1 Class 8 Maths Chapter 6 Cubes and Cube Roots

Here are some advantages of solving NCERT solutions class 8 maths chapter 6 ex 6.1 Cubes and Cube Roots on a regular basis.

1. These NCERT solutions for class 8 maths ch 6 ex 6.1 are written in a very easy-to-understand language.
2. You will learn a few quick tricks and tips that will help you solve the problem in a short period of time.
3. These solutions can be very helpful to practice questions of ex 6.1. It is recommended to attempt to solve each question, including the examples and practical questions. 
4. These class 8 maths chapter 6 ex 6.1 solutions will help you to prepare for the exam.

Frequently Asked Questions

Question 1. What is the difference between a cube and a cube root in chapter 6 ex 6.1?

Answer 1. When you multiply a number three times, you get a cube of that number. Now, you can say the given number is the cube root of the product so obtained. For example, 125 is the cube of 5 as 555 product 125 and 5 is the cube root of 125.

Question 2. Where can I find the complete solutions of NCERT for class 8 maths chapter 6 ex 6.1?

Answer 2. Here, at eSaral you will get the detailed NCERT solutions for class 8 maths chapter 6 ex 6.1.