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A group of 1536 cadets wanted to have a parade forming a square design. Is it possible? If it is not possible how many more cadets would be required?

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Number of cadets to form square design

1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

The numbers 2 and 3 are unpaired

It is impossible to have the parade forming square design with 1536 cadets.

39 x 39 = 1521

Also 40 x 40 = 1600

∴ We have to add (1600 – 1536) = 64 to make 1536 a perfect square.

∴ 64 more cadets would be required to form the square design.

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