## Intermediate Algebra (12th Edition)

$14\sqrt{2}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $7(\sqrt{50}-\sqrt{18}) ,$ simplify first each radical by extracting the root of the factor that is a perfect power of the index. Then combine like terms and multiply by $7$. $\bf{\text{Solution Details:}}$ Expressing the radicand with a factor that is a perfect power of the index, the given expression is equivalent to \begin{array}{l}\require{cancel} 7(\sqrt{25\cdot2}-\sqrt{9\cdot2}) \\\\= 7(\sqrt{(5)^2\cdot2}-\sqrt{(3)^2\cdot2}) .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 7(5\sqrt{2}-3\sqrt{2}) .\end{array} Combining the like radicals and multiplying by $7$ result to \begin{array}{l}\require{cancel} 7[(5-3)\sqrt{2}] \\\\= 7[2\sqrt{2}] \\\\= 14\sqrt{2} .\end{array}