Question

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

Answer 1

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

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