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Find the Smallest Integer Challenge

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,680
Determine the smallest integer that is square and starts with the first four figure 3005. Calculator may be used but solution by computers will not be accepted.(Tongueout)
 

kaliprasad

Well-known member
Mar 31, 2013
1,309
Determine the smallest integer that is square and starts with the first four figure 3005. Calculator may be used but solution by computers will not be accepted.(Tongueout)
we can have even number of digits.odd

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^n = 173.34 * 10^n

sqrt 30060 * 10^n= 173.37 * 10 ^n

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

17335

so it is 5482^2 = 30052324
 
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anemone

MHB POTW Director
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Feb 14, 2012
3,680
Hi kaliprasad, thanks for participating and your answer is correct!:)