Q13/ 088) Determine the smallest integer that is square and starts with the first four digits 3005.

we can have even number of digits or odd number of digits and they have to be treated separately

if even then we have

sqrt (3005 * 10^2n) = 54.8177 * 10^n
sqrt (3006* 10^2n) = 54.8270 * 10^n

if odd digits then

sqrt (30050 * 10^2n) = 173.34 * 10^n

sqrt (30060 * 10^2n)= 173.37 * 10 ^n

from the 1st set we get square root  5482 as smallest where a digit is different and from the second at least

17335

so it is 5482^2 = 30052324