Checking if perfect cube

Chapter 6 Class 8 Cubes and Cube Roots
Concept wise

Let’s do this by examples

#### Is 216 a perfect cube?

Let’s do prime factorization of 216 Thus,

216  = 2 × 2 × 2 × 3 × 3 × 3

Now,

We make groups of 3 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 We see that 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 We see that 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 We see that Since 3 does not occur in triplets

∴ 1125 is not a perfect cube.

### Is 6859 a perfect cube?

Doing Prime factorization of 6859 We see that 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 We see that 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 We see that Since 2 does not occur in triplets.

∴ 5324 is not a perfect cube.

### Is 968 a perfect cube?

Doing Prime factorization of 968 We see that Since 11 does not occur in triplets.

∴ 968 is not a perfect cube

### Is 400 a perfect cube?

Doing Prime factorization of 400 Since 2 & 5 do not occur in triplets.

∴ 400 is not a perfect cube.

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