Cubes and Cube Roots Complete Guide with Meaning and Methods

Class 8 students need to learn all chapters in the mathematics curriculum with proper care. However, you must focus more intensely on the cubes and cube roots chapter. This lesson can help you throughout your academic career, even if you choose to pursue competitive examinations in the future. 

With a proper understanding of cubes and cube roots class 8 curriculum, you can solve almost any questions that arise from this chapter. In the following lesson, students will learn about the Hardy-Ramanujan Number, prime factors and other useful factors regarding cubes.     

What is The Hardy-Ramanujan Number?

Hardy-Ramanujan number refers to any figure, which can be expressed by the summation of two cubes. For example, 1729 is not a perfect cube but you can express the same as 1728 + 1 or 123 + 13. The same number can also be expressed as 1000 + 729, which is also 103 + 93. 1729 is the smallest Hardy-Ramanujan Number. Other numbers in this series include 4104, 13832 and many more.

Properties of a Cube Number

When studying chapter 7 cubes and cube roots, one should pay close attention to the various characteristics of cubes. These properties include the following factors – 

• Cubes of all odd numbers are odd.

• Cubes of all even numbers are even.

• Cubes of numbers ending with two will end in eight. Similarly, cubes of a number ending with eight always end with two.

• Cube of a number ending with 3 will always end with 7. Also, the cube of a number ending with 7 will always end with 3.

• The sum of cubes of first ‘n’ natural numbers will always be equal to the square of their sums.

Assessing Prime Factorisation in CBSE class 8 Maths Cubes and Cube Roots

Prime factorisation is a method through which you can easily determine whether a particular figure represents a perfect cube. If each prime factor can be clubbed together in groups of three, then the number in question is a perfect cube. To understand how prime factorisation method works, let us take the help of an example.

Consider the number 500 to be divided using prime factorisation. Therefore, we can say,

500 = 2 x 2 x 5 x 5 x 5 = 22 x 53 

Now, let us consider the number 1728.

1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 23 x 23 x 33

Here, all numbers form cubes, which is why, we can say definitively that 1728 is a perfect cube number. In fact, its cube root is 12. Prime factorisation is one of the most important aspects of cubes and cube roots. Therefore, ensure you have no doubts regarding this topic.   

True or False

Q. Any cube of a natural number with 3 as its multiple will also have 27 as a multiple.

Ans. True. 

Cube Root Estimation

Let us assume a number, say 205379. Start clubbing three numbers from the right hand side. So, the first group will have 379, while the second group will have 205. Since the unit place of the first group is 9, we can say that the cube root’s unit place will also be 9. 

Next, take the second group number and determine the closest perfect cubes to it. The closest perfect cubes to 205 are 125, which is 53, and 216, which is 63. Assume the lower cube root number as the first digit for the starting number. Thus, with this method, you can arrive at the result, 59, which is indeed the cube root for 205379. 

Keep practicing cubes and cube roots exercises to gain a better understanding of this topic.       

Sky is the Limit

We can assist in your preparations, making class 8 mathematics seem simple. Even the dreaded cubes and cube roots chapter will seem easy after you attend our live classes, conducted by expert teachers from across India. Vedantu provides highest-quality, exclusive study materials. 

These papers and exercises are created with great care, enhancing your cubes and cube roots class 8 CBSE preparations, along with all other chapters. 

Join the Vedantu family today!