Q12 of 45 Page 7

Multiply 137592 by the smallest number so that the product is a perfect cube. Also, find the cube root of the product.


Solution:
137592 = 2´2´2´3´3´3´7´7´13
The number 7 and 13 should be multiplied once and twice
respectively so that the product is a perfect cube.
...  The smallest number by which 137592 must 
be multiplied = 7´13´13 = 1183 

The required product = 137592 x 1183 =  2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 13 x 7 x 13 x 13
= (23 x 33 x 73 x 133)
= (2 x 3 x 7 x 13)3


= 546

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