Question

please answer by solving
Find the least number which must be added to 97330 so that to make it a perfect square number also find the new number and its square root​

Answer 1

Answer:

Step-by-step explanation:

(i) 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.

(v) 6412

Since remainder is 12.

Therefore 80^2<641280  

2

<6412

Next perfect square number 81^2=656181  

2

=6561

Hence, number to be added

= 6561 – 6412 = 149

\therefore6412+149=6561∴6412+149=6561

Hence, the square root of 6561 is 81.