Question

3.
Find the smallest number by which 2400 is to be multiplied to get a perfect square and also
find the square root of the resulting number.
​

Answer 1

Answer:

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

Square root of 14400

          120

         ___________ 

      1 |14400

         |1

         |_____

   22  |044

         |  44  

         |______

         |   000

         |______

  Hence, √14400 = 120

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