Let’s do this by examples

 

Is 216 a perfect cube?

Let’s do prime factorization of 216

checking if perfect cube.jpg

Thus,

 216  = 2 × 2 × 2 × 3 × 3 × 3

 

Now,

We make groups of 3

Checking if perfect cube - Part 2

Since 2 & 3 occur in triplets.

∴ 216 is a perfect cube.

 

Cube root of 216 = 2 × 3

         = 6

 

Is 729 a perfect cube?

Doing Prime factorization of 729

Checking if perfect cube - Part 3

We see that

Checking if perfect cube - Part 4

 

Since 3 occurs in triplets.

∴ 729 is a perfect cube.

 

Cube root of 729 = 3 × 3

 

Is 3375 a perfect cube?

Doing Prime factorization of 3375

Checking if perfect cube - Part 5

We see that

Checking if perfect cube - Part 6

Since 3 & 5 occurs in triplets.

∴ 3375 is a perfect cube.

 

Cube root of 3375 = 3 × 5

       = 15

 

Is 1125 a perfect cube?

Doing Prime factorization of 1125

Checking if perfect cube - Part 7

We see that

Checking if perfect cube - Part 8

Since 3 does not occur in triplets

∴ 1125 is not a perfect cube.

 

Is 6859 a perfect cube?

Doing Prime factorization of 6859

Checking if perfect cube - Part 9

We see that

Checking if perfect cube - Part 10

Since 19 occurs in triplets.

∴ 6859 is a perfect cube.

 

Cube root of 6859 = 19

 

Is 10648 a perfect cube?

Doing Prime factorization of 10648

Checking if perfect cube - Part 11

We see that Checking if perfect cube - Part 12

Since 2 & 11 occurs in triplets.

∴ 10648 is a perfect cube.

 

Cube root of 10648 = 2 × 11

        = 22

 

Is 5324 a perfect cube?

Doing Prime factorization of 5324

Checking if perfect cube - Part 13

We see that

Checking if perfect cube - Part 14

Since 2 does not occur in triplets.

∴ 5324 is not a perfect cube.

 

Is 968 a perfect cube?

Doing Prime factorization of 968

Checking if perfect cube - Part 15

We see that

Checking if perfect cube - Part 16

Since 11 does not occur in triplets.

∴ 968 is not a perfect cube

 

Is 400 a perfect cube?

Doing Prime factorization of 400

Checking if perfect cube - Part 17

Since 2 & 5 do not occur in triplets.

∴ 400 is not a perfect cube.

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

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.