Cube Root
Perfect Cube
A number m is a perfect cube if there is an integer n such that m = n x n x n
Properties of Perfect Cubes
Property 1. we can see in this table if a number ends in the digits 1,4,5,6,9 its cube also ends in the digits 1,4,5,6,9.
Property 2. If a number has 2 in its units, its cube has 8 in thie units place. and vice versa if a number has 8 in its units place, its cube has 2 in the units place.
Property 3. If a number has 3 in its units, its cube has 7 in thie units place. and vice versa if a number has 7 in its units place, its cube has 3 in the units place.
Cubes of Negative Integers
The cube of negative integers are negatvie and negative integers can also be perfect cubes.
Cube Root
The cube root of a number is that number which when cubed gives the original number .
The cube root of 64 is 4, because when 4 is cubed, we get 64.
Q 1. What is the smallest number by which 4116 must be multiplied so that the product is a perfect cube ? Find the cube root of the perfect cube so obtained.
Solution : Factorising 4116, we get
4116 = 2 x 2 x 3 x 7 x 7 x 7
As factors 2 x 2 donot form a triple and also 3 donot form, so multiply 18 with 4116 will give us a perfect cube
Now, if we multiply 4116 by 18 , we get 74088
and 74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
Which is a perfect cube whose cube root is 42.
A number m is a perfect cube if there is an integer n such that m = n x n x n
Properties of Perfect Cubes
| X | x3 |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
Property 1. we can see in this table if a number ends in the digits 1,4,5,6,9 its cube also ends in the digits 1,4,5,6,9.
Property 2. If a number has 2 in its units, its cube has 8 in thie units place. and vice versa if a number has 8 in its units place, its cube has 2 in the units place.
Property 3. If a number has 3 in its units, its cube has 7 in thie units place. and vice versa if a number has 7 in its units place, its cube has 3 in the units place.
Cubes of Negative Integers
The cube of negative integers are negatvie and negative integers can also be perfect cubes.
Cube Root
The cube root of a number is that number which when cubed gives the original number .
The cube root of 64 is 4, because when 4 is cubed, we get 64.
Q 1. What is the smallest number by which 4116 must be multiplied so that the product is a perfect cube ? Find the cube root of the perfect cube so obtained.
Solution : Factorising 4116, we get
4116 = 2 x 2 x 3 x 7 x 7 x 7
As factors 2 x 2 donot form a triple and also 3 donot form, so multiply 18 with 4116 will give us a perfect cube
Now, if we multiply 4116 by 18 , we get 74088
and 74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
Which is a perfect cube whose cube root is 42.