Question

16. Find the smallest number by which 9408 should be divided by to get a perfect square. Also find the square root of the following number obtained.

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Answer 1

Answer: 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

Step-by-step explanation:

Answer 2

Answer:

3 & 56

Step-by-step explanation:

taking out the prime factorisation of the number 9408

i.e 2×2×2×2×2×2×3×7×7

The number 3is the unpaired one so 3 is the smallest number by which 9408 can be divided and the answer is 3136,

3136 its perfect square

__________

√3136 = 56