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

## NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots - Free PDF

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

Answer: 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.

NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots explain the concepts of cubes and cube roots. There are several examples in this chapter that will help you understand the steps to find cubes and cube roots. After you understand the concepts properly, you can work out the problem sums given in the exercises.

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

Answer: 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.

3. Does a cube root have a sign?

Answer: 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.

4. What are the benefits of referring to the NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots?

Answer: The NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots are available as a free PDF on Vedantu. These NCERT solutions will help the students to understand all the concepts of this chapter of cubes and cube roots clearly.

Some of the concepts explained in this chapter include the ‘smallest multiple that is a perfect cube’, ‘Cube root through prime factorization method’, ‘some interesting patterns’, ‘Cube root of a cube number’, etc.

Also, there are sums for calculating cubes and cube roots of numbers containing at most 3 digits, and for estimating the cube roots and square roots.

The exercise for this chapter consists of short answer questions, long answer questions.