Question

Find the least number which must be added to 4220 so as to get a perfect square. Also find the square root of the square number so obtained. ​

Answer 1

Answer:

525

Since remainder is 41.

Therefore 22^2<52522

2

<525

Next perfect square number 23^2=52923

2

=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<175041

2

<1750

Next perfect square number 42^2=176442

2

=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<25215

2

<252

Next perfect square number 16^2=25616

2

=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<182542

2

<1825

Next perfect square number 43^2=184943

2

=1849

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

\therefore1825+24=1849∴1825+24=1849

Hence, the square root of 1849 is 43.