Answer :
(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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