Question

find the least number that must be added to 16160 so as to get a perfect square

Answer 1

First finding the square root of 16160 by long division method;
$$\begin{gathered} 127 \\ 1\left|\overline{\overline{\overline{1}}\overline{61}\overline{60}}\right| \\ +1\left|1\right| \\ \overline{22\left|061\right|} \\ +2\left|44\right| \\ \overline{247\left|1760\right|} \\ 1729 \\ \overline{31} \end{gathered}$$
So, the remainder is 31.
And ${\left(127\right)}^2=16129$
So, ${\left(127\right)}^2<16160$
Next perfect square number is ${\left(128\right)}^2=16384$
Hence the least number to be added is ${\left(128\right)}^2-16160$
$\Rightarrow 16384-16160=224$