# 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

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 root of the perfect square so obtained.
(a) 2361 (b) 612858​

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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

= 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

= 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

= 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