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

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## Chapter 7 : Cubes And Cube Roots

### 7.1 Introduction

This is a story about one of India’s great mathematical geniuses, S. Ramanujan. Once another famous mathematician Prof. G.H. Hardy came to visit him in a taxi whose number was 1729. While talking to Ramanujan, Hardy described this number “a dull number”. Ramanujan quickly pointed out that 1729 was indeed interesting. He said it is the smallest number that can be expressed as a sum of two cubes in two different ways:
1729 has since been known as the Hardy – Ramanujan Number, even though this feature of 1729 was known more than 300 years before Ramanujan.
How did Ramanujan know this? Well, he loved numbers. All through his life, he experimented with numbers. He probably found numbers that were expressed as the sum of two squares and sum of two cubes also.
There are many other interesting patterns of cubes. Let us learn about cubes, cube roots and many other interesting facts related to them.

### 7.2 Cubes

You know that the word ‘cube’ is used in geometry. A cube is a solid figure which has all its sides equal. How many cubes of side 1 cm will make a cube of side 2 cm? How many cubes of side 1 cm will make a cube of side 3 cm? Consider the numbers 1, 8, 27, ... These are called perfect cubes or cube numbers. Can you say why they are named so? Each of them is obtained when a number is multiplied by itself three times.

### 7.3 Cube Roots

If the volume of a cube is 125 cm3, what would be the length of its side? To get the length of the side of the cube, we need to know a number whose cube is 125. Finding the square root, as you know, is the inverse operation of squaring. Similarly, finding the cube root is the inverse operation of finding cube.

### Smartur

Learning is (Super) rewarding!