Let’s do this by examples

Finds the smallest number divided to 1125 to get a perfect cube

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We see that,

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Since 3 does not occur triplets,

we divide by 3 × 3 to make a triplet

 

So, our number becomes

1125 × 1/ 3 × 1/3   = 3 × 3 × 5 × 5 × 5 × 1/3 × 1/3

     = 5 × 5 × 5

 

Now, it becomes a perfect cube.

 

So, we divide 1125 by 3 × 3

i.e. 9 to make it a perfect cube

 

Finds the smallest number divided to 5324 to get a perfect cube.

22.jpg

We see that,

  5324 = 2 × 2 × 11 × 11 × 11

 

Here,

2 does not occur in triplets

So, we divide by 2 × 2 to make triplet

 

So, our number becomes

  5324  × 1/2  × 1/2 = 2 × 2 × 11 × 11 × 11 × 1/2   × 1/2

       = 11 × 11 × 11

 

Now, it becomes a perfect cube.

 

So, we divide 5324 by 2 × 2

i.e. to make it a perfect cube

 

Finds the smallest number divided to 968 to get a perfect cube.

23.jpg

 

We see that,

  968 = 2 × 2 × 2 × 11 × 11

 

Here,

11 does not occur in triplets

So, we divide by 11 × 11 to make triplet

 

So, our number becomes

  400 × 1/2  × 1/ 5 × 1/5 = 2 × 2 × 2 × 2 × 5 × 5 × 1/2   × 1/5 × 1/5

          = 2 × 2 × 2

 

Now, it becomes a perfect cube.

 

So, we divide 400 by 2 × 5 × 5

i.e. 50  to make it a perfect cube

 

So, our number becomes

  400 × 1/2  × 1/ 5 × 1/5 = 2 × 2 × 2 × 2 × 5 × 5 × 1/2   × 1/5 × 1/5

          = 2 × 2 × 2

 

Now, it becomes a perfect cube.

 

So, we divide 400 by 2 × 5 × 5

i.e. 50  to make it a perfect cube

  1. Chapter 7 Class 8 Cubes and Cube Roots
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.