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
3√137592×1183=2×3×7×13
=546