# Write true (T) or

(i) 392 is a perfect cube.

False.

Prime factors of 392 = 2 × 2 × 2 × 7 × 7 = 23 × 72

(ii) 8640 is not a perfect cube.

True

Prime factors of 8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 23 × 23 × 33 × 5

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

True

Beause a perfect cube always have zeros in multiple of 3.

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

False

64 is a perfect cube = 4 × 4 × 4 and it ends with 4.

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

False

In case of negative integers ,

=

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

False

In case of negative integers,

=

But ,

(vii) If a divides b, then a3 divides b3.

True

If a divides b =

=

For each value of b and a its true.

(viii) If a2 ends in 9, then a3 ends in 7.

False

Let a = 7

72 = 49 and 73 = 343

(ix) If a2 ends in an even number of zeros, then a3 ends in 25.

False

Let a = 20

= a2 = 202 = 400 and a3 = 8000

(x) If a2 ends in an even number of zeros, then a3 ends in an odd number of zeros.

False

Let a = 100

= a2 = 1002 = 10000 and a3 = 1003 = 1000000

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