Two airplanes are spotted on a radar map located at the coordinates (2√2 , - √5 ) and (3√2 , 5√5 ). Determine the distance the airplanes are

Two airplanes are spotted on a radar map located at the coordinates (2√2 , - √5 ) and (3√2 , 5√5 ). Determine the distance the airplanes are apart using a calculator to state your answer in decimal form to the nearest hundreds. Assume the coordinates are given so that the distance is in units of miles

$$\binom{x_1}{y_1}=\binom{2\sqrt{2}}{-\sqrt{5}} \qquad \binom{x_2}{y_2}=\binom{3\sqrt{2}}{5\sqrt{5}}$$

$$\boxed{\rm{distance}~&=& \sqrt { (x_2-x_1)^2 + (y_2-y_1)^2 }}\\\\ \small{\text{$ \begin{array}{rcl} \rm{distance}~&=& \sqrt { ( 3\sqrt{2} - 2\sqrt{2})^2 + [ 5\sqrt{5} - (-\sqrt{5}) ]^2 } \\\\ \rm{distance}~&=& \sqrt { ( 3\sqrt{2} - 2\sqrt{2})^2 + [ 5\sqrt{5} + \sqrt{5} ]^2 } \\\\ \rm{distance}~&=& \sqrt { (\sqrt{2})^2 + ( 6\sqrt{5} )^2 } \\\\ \rm{distance}~&=& \sqrt { 2 + 36\cdot 5 } \\\\ \rm{distance}~&=& \sqrt { 182} \\\\ \rm{distance}~&=& 13.4907375632 \\\\ \rm{distance}~&\approx& 13.49 ~\rm{miles} \end{array} $}}$$