How many non-square numbers lie between the following pairs of numbers?

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Uniteasy Admin · Accepted Answer

The numbers between squares of two consecutive numbers are all non-perfect squares.$$100^2$$ and $$101^2$$
$$101^2-100^2 = (101-100)(101+100) = 201$$
Therefore, there are 200 non-square numbers between $$100^2$$ and $$101^2$$ $$999^2$$ and $$1000^2$$
$$1000^2-999^2=(1000-999)(1000+999) = 1999$$
Therefore, there are 1998 non-square numbers between $$999^2$$ and $$1000^2$$ $$11^2 $$ and $$12^2$$
$$12^2-11^2 =(12-11)(12+11) = 23$$
Therefore, there are 22 non-square numbers between $$11^2 $$ and $$12^2$$

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