Question

Is 9800 a perfect cube? If not, find the smallest number by which 9800

must be multiplied to get a perfect cube. Also, find the cube root of the new

number.
please solve showing all the workings​

Answer 1

No, 9800 is not a perfect cube. 35 is the smallest number by which 9800  must be multiplied to make it a perfect cube. 70 would be the cube root of the new number.

Step-by-step explanation:

No, 9800 is not a perfect cube.

To find the smallest number by which 9800 to be multiplied in order to make it a perfect square, We need to find the L.C.M. of 9800;

9800 = 2 * 2 * 2 * 5 * 5 * 7 * 7

Thus, 5 * 7 = 35 is the number that should be multiplied to 9800 to make it a perfect cube.

The new number is;

9800 * 35 = 3,43,000

3,43,000 = 2 * 2 * 2 * 5 * 5 * 5 * 7 * 7 * 7

= 2 * 5 * 7

= 70

∵ $\sqrt[3]{343000}$ = 70

Learn more: Cube root

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