Question

Find the smallest number by which 9408 must be divided so that the quotient is a perfect square.  Find the square root of the quotient

Answer 1

Solution :-

To find the smallest number by which 9408 must be divided so that the quotient is a perfect square, we have to find the prime factors of 9408.

9408 = 2*2*2*2*2*2*3*7*7

Prime factors of 9408 are 2, 2, 2, 2, 2, 2. 3, 7, 7
Out of the prime factors of 9408, only 3 is without pair.
So, 3 is the number by which 9408 must be divided to make the quotient a perfect square.

9408/3 = 3136

Square root of 3136

              56
        _____________
   5   |    3136
   5   |    25
___  |______
106  |      636
   6   |      636
        |_______
        |      000
       
So, √3136 = 56

Answer.