Q. 34.0( 4 Votes )

Let us write whic

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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