Q. 235.0( 2 Votes )

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.

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

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

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

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

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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