Question

Find the smallest number by which 9408 must be divided so that it become a perfect square . Also find the square root of the number so obtained

Answer 1

Answer:

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Step-by-step explanation:

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 2

Answer:

$9408 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 7 \times 7 = {2}^{6} \times 3 \times {7}^{2}$

so required smallest number = 3.

square root of obtained number =

$\sqrt{ {2}^{6} \times {7}^{2} } = {2}^{3} \times 7 = 8 \times 7 = 56$