Q. 235.0( 2 Votes )

Write true (T) or

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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