find the least number which must be added to each of the following number so as to get a perfect square. Also find the square roo

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1. Step-by-step explanation:

   (i) 525

   Since remainder is 41.

   Therefore 22^2<525222<525

   Next perfect square number 23^2=529232=529

   Hence, number to be added

   = 529 – 525 = 4

   \therefore525+4=529∴525+4=529

   Hence, the square root of 529 is 23.

   

   (ii) 1750

   Since remainder is 69.

   Therefore 41^2<1750412<1750

   Next perfect square number 42^2=1764422=1764

   Hence, number to be added

   = 1764 – 1750 = 14

   \therefore1750+14=1764∴1750+14=1764

   Hence, the square root of 1764 is 42

   

   (iii) 252

   Since remainder is 27.

   Therefore 15^2<252152<252

   Next perfect square number 16^2=256162=256

   Hence, number to be added

   = 256 – 252 = 4

   \therefore252+4=256∴252+4=256

   Hence, the square root of 256 is 16.

   

   (iv) 1825

   Since remainder is 61.

   Therefore 42^2<1825422<1825

   Next perfect square number 43^2=1849432=1849

   Hence, number to be added = 1849 – 1825 = 24

   \therefore1825+24=1849∴1825+24=1849

   Hence, the square root of 1849 is 43.

   

   (v) 6412

   Since remainder is 12.

   Therefore 80^2<6412802<6412

   Next perfect square number 81^2=6561812=6561

   Hence, number to be added

   = 6561 – 6412 = 149

   \therefore6412+149=6561∴6412+149=6561

   Hence, the square root of 6561 is 81.

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