[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
C&({{ 3}}\quad ,&{{ 8}})\quad
% (c,d)
D&({{ 6}}\quad ,&{{ -1}})
\end{array}\qquad
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
CD=\sqrt{(6-3)^2+(-1-8)^2}\implies CD=\sqrt{3^2+(-9)^2}
\\\\\\
CD=\sqrt{9+81}\implies CD=\sqrt{90}\quad
\begin{cases}
90=2\cdot 3\cdot 3\cdot 5\\
\qquad 2\cdot 3^2\cdot 5\\
\qquad 10\cdot 3^2
\end{cases}
\\\\\\
CD=\sqrt{10\cdot 3^2}\implies CD=3\sqrt{10}[/tex]
