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.