Question

A(i) find the smallest number by which 1323 must be multiply so that the product is a perfect cube.(ii) What is the smallest number by which 1600 must be divided so that the question is a perfect cube? (iii) The volume of a cubical box is13.824 cubic meters .find the length of each side of the box.

Answer 1

(i) 1323 = 3 * 3 * 3 * 7 * 7

             = 3^3 * 7^2.

In this factorization, there is no triplet for 7.

So 1323 is not a perfect cube.

To make it a perfect cube it be multiplied by 7.




(ii) 1600 = 2 * 2 * 2 * 2 * 2 * 2 * 5 * 5

              = (2^3) * (2^3) * 5^2

              = (2 * 2)^3 * 5^2

In this factorization, there is no triplet for 5.

So it is not a perfect cube.

To make it a perfect cube it should be divided by 25.



(iii) Given volume of a cube = 13.824 m^3.

Let the side of the cube = x.

We know that volume of a cube = s^3

                                      x^3 = 13.824

                                      x = 2.4.

The length of each side of the box = 2.4m.


Hope this helps!