## NCERT Solution for Maths Class 8 Cubes and Cube Roots Chapter 6 - FREE PDF Download

## FAQs on NCERT Solutions for Class 8 Maths Chapter 6 Cubes and Cube Roots

1. What is a cube root?

Cube root is the value that, when multiplied by itself three times, gives us a required number. To denote this using an example, 9 X 9 X 9 gives us 729. In this example, 9 is the cube root of 729. Similarly, 729 is the cube of 9.

Cube roots are represented symbolically using the symbol ∛. So, for the example given above, it is represented as ∛729 = 9.

2. What is the difference between a cube and a cube root?

When a number is multiplied by itself three times, the product so obtained is called the cube of the number. Now, you can say that the given number is the cube root of the product so obtained. For example, 27 is the cube of 3, as 3 x 3 x 3 gives 27; and 3 is the cube root of 27.

3. Does a cube root have two solutions like a square root?

No, cube roots do not have two solutions. A square root has two solutions, one positive and the other negative, but cube roots have only one solution. For example, the solutions for the square root of 16 are +4 and -4, that is, if you multiply +4 x +4 you will get 16 and if you multiply -4 x -4, the product will be 16. But there is a unique solution for every cube root. For example, if you multiply 3 x 3 x 3, the product will be +27, but if you multiply -3 x -3 x -3, the product will not be +27, instead, the product will be -27. Hence, +3 is the cube root of +27 and -3 is the cube root of -27.

4. Does a cube root have a sign?

Yes, the cube root of any given number will have the sign of the number itself. The cube root of any number can be positive or negative or zero. To find the cube root of a given number, you have to identify the prime factors of the number that are multiplied thrice to get the number. And if the given number has a positive or negative sign, then the cube root will have the same sign as the number itself.

For example, if the cube root of -216 has to be calculated, then the prime factors of 216 have to be found first, (2 x 2 x 2 x 3 x 3 x 3). Now keeping the negative sign outside the parentheses, it becomes - (2 x 2 x 2 x 3 x 3 x 3). Here, the prime factors can be divided into two groups of three common numbers, that is,

- {(2 x 2 x 2) x (3 x 3 x 3)}. So, the cube root is - (2 x 3) = -6. If the given number was +216, then the cube root would have been +6.

5. What are the different methods of finding the cube root of a given number?

Chapter 7 "Cube and Cube Roots" teaches us two main methods of finding cube roots of a given number:

Cube root through prime factorization method

Cube root when you know a number is a cube number

These methods are explained in great detail in Vedantu's NCERT Solutions for Chapter 7 of Class 8 Maths. Here, you can find the two methods mentioned above explained by our expert teachers using simple examples.

6. What is a Cube of a number in class 8 maths Cube and Cube Roots ?

A Cube of a number is the result of multiplying the number by itself twice more. For example, if the number is n, then its Cube is n×n×n. This concept is fundamental in understanding cubic numbers and their properties. Cubes are used in various mathematical applications and geometric calculations.

7. What is a perfect Cube in class 8 maths Cube and Cube Roots ?

A perfect Cube is a number that can be expressed as the Cube of an integer. For instance, 27 is a perfect Cube because it can be written as 3×3×3. Recognizing perfect Cubes is important for solving problems related to volume and other cubic measurements. Perfect Cubes also help in simplifying complex algebraic expressions.

8. How do you find the Cube Roots of a number in class 8 maths chapter 6?

The Cube Root of a number is found by determining which number, when multiplied by itself three times, gives the original number. For example, the Cube Root of 27 is 3 because 3×3×3=27. This concept is essential for solving equations involving cubic terms and for various real-world applications like volume calculations.

9. What is the prime factorization method for finding Cube Roots in ncert class 8 maths chapter 6 ?

Prime factorization involves breaking down the number into prime factors, grouping them in sets of three, and taking one factor from each group. For example, to find the Cube Root of 64, you break it down to 2×2×2×2×2×2, group them into sets of three (2×2×2) and take one factor from each group, resulting in 2 3 =8. This method simplifies finding Cube Roots for large numbers.

10. What types of questions are in class 8 maths chapter 6 pdf solutions?

Exercise 6.2 includes questions on calculating Cube Roots using prime factorization. Students are required to break down numbers into their prime factors, group them accordingly, and then find the Cube Root. These questions help reinforce the understanding of Cube Roots and prime factorization, providing practical skills in number manipulation and problem-solving.

11. What is covered in ncert class 8 maths chapter 6?

Exercise 6.1 focuses on finding the Cubes of given numbers and identifying perfect Cubes. Students learn to calculate the Cube of a number and recognize which numbers are perfect Cubes. This exercise builds a foundation for understanding cubic relationships and prepares students for more complex operations involving Cubes and Cube Roots.

12. How many questions from this chapter appeared in previous exams from ncert class 8 maths chapter 6 ?

Three questions from this chapter appear in exams, focusing on both theoretical understanding and practical application. These questions typically involve finding Cubes, identifying perfect Cubes, and calculating Cube Roots using different methods. This highlights the importance of mastering these concepts for academic success and practical problem-solving.