NCERT Solutions for Cube and Cube Root Class 8 Maths Chapter 7 - Free PDF Download
FAQs on NCERT Solutions for Class 8 Maths Chapter 7 - 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.