Question

Write true (T) or false (F) for the following statements:

(i) 392 is a perfect cube.

(ii) 8640 is not a perfect cube.

(iii) No cube can end with exactly two zeros.

(iv) There is no perfect cube which ends in 4.

(v) For an integer a, a³ is always greater than a².

(vi) If a and b are integers such that a² > b², then a³ >b³.

Answer 1

(i) 392 is a perfect cube.

 392 = 2 × 2 × 2 × 7 × 7 

= 2³ × 7²

Hence the statement is False.

(ii) 8640 is not a perfect cube.

 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 

= 2³ × 2³ × 3³ × 5

Hence the statement is True

(iii) No cube can end with exactly two zeros. Because a perfect cube always have zeros in multiple of 3.

 Statement is True.

(iv) There is no perfect cube which ends in 4.

4 × 4 × 4 and it ends with 4.

Hence the statement is False.

(v) For an integer a, a³ is always greater than a².

Because in case of negative integers ,

(-2)² = 4 and (-2)³ = -8

Statement is False.

(vi) If a and b are integers such that a²>b², then a³>b³.

In case of negative integers,

(-5)² > (-4)² = 25 > 16

But, (-5)³ > (-4)³ = -125 > -64 is not true.

Statement is False.