Answer
$=-6\sqrt{2}$
$\approx -8.49$
Work Step by Step
The given function is
$=-\sqrt{2a^2+b^2}$
Substitute $-2$ for $a$ and $8$ for $b$.
$=-\sqrt{2(-2)^2+(8)^2}$
Simplify.
$=-\sqrt{8+64}$
$=-\sqrt{72}$
Factor as square term.
$=-\sqrt{36\cdot 2}$
$=-\sqrt{6^2\cdot 2}$
Use product property of square roots.
$=-\sqrt{6^2}\cdot \sqrt{2}$
Simplify.
$=-6\sqrt{2}$
Rounded to the nearest hundredth.
$\approx -8.49$
