Answer :

Let us understand what perfect cube is.

A perfect cube is a number that is the cube of an integer.

**(i).** Let us check for 216.

We need to check whether 216 is a cube of an integer or not.

Let us factorize 216 for ease of calculation.

We have,

216 = 2 × 2 × 2 × 3 × 3 × 3

Group these factors into three similar integers.

216 = (2 × 2 × 2) × (3 × 3 × 3)

Take cube root on both sides,

Cube root of 216 is an integer.

**Thus, 216 is a perfect cube.**

**(ii).** Let us check for 343.

We need to find whether 343 is cube of an integer or not.

Let us factorize 343 for ease of calculation.

We have,

343 = 7 × 7 × 7

Group these factors into three similar integers.

343 = (7 × 7 × 7)

Take cube root on both sides,

Cube root of 343 is an integer.

**Thus, 343 is a perfect cube.**

**(iii).** Let us check for 1024.

We need to find whether 1024 is cube of an integer or not.

Let us factorize 1024 for ease of calculation.

We have,

1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Group these factors into three similar integers.

1024 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 2

Take cube root on both sides,

Cube root of 1024 is clearly not an integer, since is not an integer.

**Thus, 1024 is not a perfect cube.**

**(iv).** Let us check for 324.

We need to find whether 324 is cube of an integer or not.

Let us factorize 324 for ease of calculation.

We have,

324 = 2 × 2 × 3 × 3 × 3 × 3

Group these factors into three similar integers.

324 = (3 × 3 × 3) × 2 × 2 × 3

Take cube root on both sides,

Cube root of 324 is clearly not an integer, since is not an integer.

**Thus, 324 is not a perfect cube.**

**(v).** Let us check for 1744.

We need to find whether 1744 is cube of an integer or not.

Let us factorize 1744 for ease of calculation.

We have,

1744 = 2 × 2 × 2 × 2 × 109

Group these factors into three similar integers.

1744 = (2 × 2 × 2) × 2 × 109

Take cube root on both sides,

Cube root of 1744 is clearly not an integer, since is not an integer.

**Thus, 1744 is not a perfect cube.**

**(vi).** Let us check for 1372.

We need to find whether 1372 is cube of an integer or not.

Let us factorize 1372 for ease of calculation.

We have,

1372 = 2 × 2 × 7 × 7 × 7

Group these factors into three similar integers.

1372 = (7 × 7 × 7) × 2 × 2

Take cube root on both sides,

Cube root of 1372 is clearly not an integer, since is not an integer.

**Thus, 1372 is not a perfect cube.**

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