Find the least number which must be subtracted from 9878 to obtain a perfect square .
Also find the square root of the number so obtained.
Answers
Answer:
(i) 525
(ii) 1750
(iii) 252
(iv) 1825
(v) 6412
Step-by-step explanation:
(i) 525
Since remainder is 41.
Therefore 22^2<525
Next perfect square number 23^2=529
Hence, number to be added
= 529 – 525 = 4
\therefore525+4=529
Hence, the square root of 529 is 23.
(ii) 1750
Since remainder is 69.
Therefore 41^2<1750
Next perfect square number 42^2=1764
Hence, number to be added
= 1764 – 1750 = 14
\therefore1750+14=1764
Hence, the square root of 1764 is 42
(iii) 252
Since remainder is 27.
Therefore 15^2<252
Next perfect square number 16^2=256
Hence, number to be added
= 256 – 252 = 4
\therefore252+4=256
Hence, the square root of 256 is 16.
(iv) 1825
Since remainder is 61.
Therefore 42^2<1825
Next perfect square number 43^2=1849
Hence, number to be added = 1849 – 1825 = 24
\therefore1825+24=1849
Hence, the square root of 1849 is 43.
(v) 6412
Since remainder is 12.
Therefore 80^2<6412
Next perfect square number 81^2=6561
Hence, number to be added
= 6561 – 6412 = 149
\therefore6412+149=6561
Hence, the square root of 6561 is 81.