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

2.jpg

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

4.jpg

We see that

3.jpg

 

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

5.jpg

We see that

6.jpg

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

7.jpg

We see that

8.jpg

Since 3 does not occur in triplets

∴ 1125 is not a perfect cube.

 

Is 6859 a perfect cube?

Doing Prime factorization of 6859

9.jpg

We see that

10.jpg

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

11.jpg

We see that 12.jpg

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

13.jpg

We see that

14.jpg

Since 2 does not occur in triplets.

∴ 5324 is not a perfect cube.

 

Is 968 a perfect cube?

Doing Prime factorization of 968

15.jpg

We see that

16.jpg

Since 11 does not occur in triplets.

∴ 968 is not a perfect cube

 

Is 400 a perfect cube?

Doing Prime factorization of 400

17.jpg

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.