Question

How many non square numbers lie between 36 square and 37 square

Answer 1

$\textbf{To find:}$

$\textsf{Number of Non square numbers between}$

$\mathsf{36^2\;and\;37^2}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{36^2=1296}$

$\mathsf{37^2=1369}$

$\textsf{The non-square numbers between}\;\mathsf{36^2\;and\;37^2\;are}$

$\mathsf{1297,1298,..........,1368}$

$\underline{\textsf{Number of terms:}}$

$\mathsf{=\dfrac{l-a}{d}+1}$

$\mathsf{=\dfrac{1368-1297}{1}+1}$

$\mathsf{=71+1}$

$\mathsf{=72}$

$\therefore\textsf{There are 72 non-square numbers between}\;\mathsf{36^2\,and\,37^2}$

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