Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set - Page 676: 8

$c=2\sqrt{41} \\\\ c\approx12.806 $

In the given right triangle, $a$ and $b$ are the legs and $c$ is the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ a=8 $ and $ b=10 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 8^2+10^2=c^2 \\\\ 64+100=c^2 \\\\ 164=c^2 \\\\ c=\sqrt{164} \\\\ c=\sqrt{4\cdot41} \\\\ c=\sqrt{(2)^2\cdot41} \\\\ c=2\sqrt{41} \\\\ c\approx12.806 .\end{array}