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Question

Multiply 137592 by the smallest number so that the product is a perfect cube. Also, find the cube root of the product.  [4 MARKS]


Solution

Concept: 1 Mark
Application: 3 Marks

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 smalest number by which 137592 must be multiplied
=7×13×13=1183

The required product
=137592×1183=2×2×2×3×3×3×7×7×13×7×13×13

=(23×33×73×133)

=(2×3×7×13)3


3137592×1183=2×3×7×13

=546

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