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8. By what smallest number should I0584 be multiplied so that the product may be a perfect square.

tell me i

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1. Step-by-step explanation:

   Prime factorisation of 10584 is

   10584=2

   3

   ×3

   2

   ×7

   2

   Now for the above to be a perfect square we can see that we need to multiply 2×3=6

   ∴ the least number to be multiplied to 10584 to make it a perfect square is 6

   ∴10584×6=2

   3

   ×3

   3

   ×7

   2

   ×2×3=2

   4

   ×3

   4

   ×7

   2

   The square root of this new number is

   2

   4

   ×3

   4

   ×7

   2

   =2

   2

   ×3

   2

   ×7

   =4×9×7

   =63×4

   =192

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