Let’s do this by examples

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

24.jpg

We see that,

  1125  = 3 × 3 × 5 × 5 × 5

 

Since 3 does not occur triplets,

we multiply by 3 to make a triplet

 

So, our number becomes

  1125 × 3   = 3 × 3 × 5 × 5 × 5 × 3

                  = 3 × 3 × 3 × 5 × 5 × 5

 

Now, it becomes a perfect cube.

 

So, we multiply 1125 by 3 to make it a perfect cube

 

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

25.jpg

We see that,

  5324 = 2 × 2 × 11 × 11 × 11

 

Here,

2 does not occur in triplets

So, we multiply by 2 to make triplet

 

So, our number becomes

    5324  × 2 = 2 × 2 × 11 × 11 × 11 × 2

    = 2 × 2 × 2 × 11 × 11 × 11

 

Now, it becomes a perfect cube.

 

So, we multiply 5324 by 2 to make it a perfect cube

 

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

26.jpg

We see that,

  968 = 2 × 2 × 2 × 11 × 11

 

Here,

11 does not occur in triplets

So, we multiply by 11 to make triplet

 

So, our number becomes

  968 × 11 = 2 × 2 × 2 × 11 × 11 × 11

 

Now, it becomes a perfect cube.

 

So, we multiply 968 by 11 to make it a perfect cube

 

Finds the smallest number divided to 400 to get a perfect cube.

27.jpg

We see that,

400  = 2 × 2 × 2 × 2 × 5 × 5

 

Here,

2 & 5 does not occur in triplets

So, we multiply by 2 × 2 × 5 to make triplet

 

So, our number becomes

  400 × 2 × 2 × 5 = 2 × 2 × 2 × 2 × 5 × 5 × 2 × 2 × 5

           = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5

 

Now, it becomes a perfect cube.

 

So, we multiply 400 by 2 × 2 × 5

i.e. 20  to make it a perfect cube

  1. Chapter 7 Class 8 Cubes and Cube Roots
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.