#### Answer

87.6

#### Work Step by Step

$66^2+56^2=x^2$
$4356+3136=x^2$
$\sqrt {7672}=x$
$\sqrt {7672}\approx90$
Divide and average to refine the approximation.
$7672\div90=85.244$
$(90+85.244)\div2=87.622$
Repeat to further refine.
$7672\div87.622=87.558$
$(87.622+87.558)\div2=87.590$