UPSC CDS 1 2022 Math Paper

Given :
194480+n=m4
Concept used :
When we square a number, on squaring the unit digit can only be 0,1,4,5,6,9
Calculations :
We know that,
On squaring, the unit digit can only be 0,1,4,5,6,9
Thus, a number of squares never have 2,3,7, and 8 as unit digit
Equation (1) can be written as
194480+n=(m2)2
When we again square the number 0,1,4,5,6,9, we get unit digit as 0,1,6,5 only.
Putting n=1 in equation (1), we get
⇒194480+1=(m2)2
⇒(√‌194481)=m2
⇒√‌441=m
⇒m=21
∴ The least value of n is 1 .