Question

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

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

Answer.

Answer 2

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