Question

EXAMPLE 28 Find the smallest number
which 2400 should be divided to make
perfect cube
a) 220 (0) 300 (0) 385 280

Pls Give the whole solution​

Answer 1

Solution:-

Prime factorization of 2400 

     2 |2400

        |_________

     2 |1200    

        |_________

     2 | 600

        |_________

     2 | 300

        |_________

     2 | 150

        |_________

     3 |  75

        |_________

     5 |  25

        |_________

     5 |   5

        |_________

        |   1

        |

2400 = 2*2*2*2*2*3*5*5

There are one 2 and one 3 in the above which are without any pair.

Therefore, the smallest number is 2*3 = 6, by which 2400 is to be multiplied to get a perfect square.

Resulting number = 2400*6 = 14400

Answer 2

300 is the smallest number.