## Elementary Algebra

$33\sqrt{2}$
Using the properties of radicals, the given expression, $7\sqrt{32}+5\sqrt{2} ,$ simplifies to \begin{array}{l}\require{cancel} 7\sqrt{16\cdot2}+5\sqrt{2} \\\\= 7\sqrt{(4)^2\cdot2}+5\sqrt{2} \\\\= 7\cdot4\sqrt{2}+5\sqrt{2} \\\\= 28\sqrt{2}+5\sqrt{2} \\\\= 33\sqrt{2} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.