Cubes

Chapter 7 Class 8 Cubes and Cube Roots
Concept wise

Let’s look at the cube of numbers from 1 to 50

 Number Cube 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000 11 1331 12 1728 13 2197 14 2744 15 3375 16 4096 17 4913 18 5832 19 6859 20 8000 21 9261 22 10648 23 12167 24 13824 25 15625 30 27000 35 42875 40 64000 45 91125 50 125000

Let’s see some pattern in it, and find properties of cube numbers

Number of zeroes at the end of a perfect cube is always multiple of 3

So, number of zeroes at the end can be 3, 6, 9, 12, 15,....

Example

• 1,000 is a perfect cube
• 8,000 is a perfect cube
• 27,000,000 is a perfect cube
• 64,000,000,000 is a perfect cube
• 20 is not a perfect cube
• 400 is not a perfect cube
• 80,000 is not a perfect cube

Cube of even numbers are always even,

Cube of odd numbers are always odd

Example :

Cube of 2 is 8,

Cube of 6 is 216

And

Cube of 7 is 343

Cube of 9 is 729

## Unit digit of cube of any number will be the unit digit of the cube of its last digit

Check Explanation

## The cube of a negative integer is always negative

Example

(-1) 3 = (-1) × (-1) × (-1) = -1

(-2) 3 = (-2) × (-2) × (-2) = -8

## The sum of the cubes of first in  natural numbers is equal to the square of their sum

1 3 + 2 3 + 3 2 +..........+ n 3 = (1 + 2 + 3 +..........+ n) 2

Example

1 3 + 2 2 + 3 3 + 4 3 = (1 + 2 + 3 + 4) 2

1 + 8 + 27 + 64 = (10) 2

100 = 100

## Cubes of the number ending in digit 1, 4, 5, 6 and 9 are the numbers ending in the same digit

 Number Cube 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000

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