#### Answer

$s=4$

#### Work Step by Step

$\sqrt {2s+8}=s$
$(\sqrt {2s+8})^2=s^2$
$2s+8=s^2$
$2s+8-2s-8=s^2-2s-8$
$s^2-2s-8=0$
$(s+2)(s-4)=0$
$s+2=0$
$s=-2$ (we can't have the square root of a number be negative, so this answer is not valid)
$s-4= 0$
$s=4$
$\sqrt {2s+8}=s$
$\sqrt {2*4+8}=4$
$\sqrt {8+8}=4$
$\sqrt {16} = 4$
$4=4$