Question

How many non square lie between 90square and 91square

Answer 1

902=8100902=8100 and 912=8281912=8281. (Even without a calculator this should be easy to do on paper or mentally.)

Therefore the non-squares in-between them are 8101, 8102, … 8279 and 8280, and there are 8280−8101+1=1808280−8101+1=180 of them

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Answer 2

$= 91 + 90 \\ = 181\: non \: square \: numbers\\ \\ proof \\ = {91}^{2} - {90}^{2} \\ = 8281 - \: 8100 \\ = 181 \\ hence \: proved$