Question

1. Find the smallest number which when multiplied with 137592 will make the product a perfect cube.

Further, find the cube root of the product.​

Answer 1

Step-by-step explanation:

The prime factors for 137592= 2×2×2×3×3×3×7×7×13

=(2×2×2)×(3×3×3)×(7×7)×(13)

for it to become a perfect cube, we need 7, 13 ,13. (then it becomes

(2cube ×3cube×7cube×13cube))

therefore 7×13×13= 1183 is the smallest number that has to be multiplied by 137592 so that the result becomes a perfect cube.

cube root of product= 2×3×7×13=546