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 
 
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.
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