Question

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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.

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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 = 56answer

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