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

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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.

Smallest number multiplied to get a perfect cube - Part 2

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.

Smallest number multiplied to get a perfect cube - Part 3

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.

Smallest number multiplied to get a perfect cube - Part 4

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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.