Q. 34.2( 99 Votes )

Find the smallest

Answer :

(i) 81 = 3 x 3 x 3 x 3

Here, one 3 is left which is not forming a triplet.


So, if we divide 81 by 3, then it will become a perfect cube


Therefore,


= 27 = 3 x 3 x 3 is a perfect cube


Hence, the smallest number by which 81 should be divided to make it a perfect cube is 3


(ii) 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2


Here, one 2 is left which is not forming a triplet.


Si, if we divide 128 by 2, then it will become a perfect cube


Therefore,


= 64 = 2 x 2 x 2 x 2 x 2 x 2 is a perfect cube


Hence, the smallest number by which 128 should be divided to make it a perfect cube is 2


(iii) 135 = 3 x 3 x 3 x 5


Here, one 5 is left which is not forming a triplet.


So, if we divide 135 by 5, then it will become a perfect cube


Therefore,


= 27 = 3 x 3 x 3 is a perfect cube


Hence, the smallest number by which 135 should be divided to make it a perfect cube is 5


(iv) 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3


Here, one 3 is left which is not forming a triplet.


So, if we divide 192 by 3, then it will become a perfect cube


Therefore,


= 64 = 2 x 2 x 2 x 2 x 2 x 2 is a perfect cube


Hence, the smallest number by which 192 should be divided to make it a perfect cube is 3


(v) 704 = 2 x 2 x 2 x 2 x 2 x 2 x 11


Here, one 11 is left which is not forming a triplet.


So, if we divide 704 by 11, then it will become a perfect cube.


Therefore,


= 64 = 2 x 2 x 2 x 2 x 2 x 2 is a perfect cube


Hence, the smallest number by which 704 should be divided to make it a perfect cube is 11


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