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
Answers
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.