Intermediate Algebra (12th Edition)

$4\sqrt{2}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\sqrt{50}-\sqrt{98}+\sqrt{72} ,$ simplify each term by extracting the root of the factor that is a perfect power of the index. Then combine like terms. $\bf{\text{Solution Details:}}$ Writing the radicand as an expression that contains a factor that is a perfect power of the index and extracting the root of that factor result to \begin{array}{l}\require{cancel} \sqrt{25\cdot2}-\sqrt{49\cdot2}+\sqrt{36\cdot2} \\\\= \sqrt{(5)^2\cdot2}-\sqrt{(7)^2\cdot2}+\sqrt{(6)^2\cdot2} \\\\= 5\sqrt{2}-7\sqrt{2}+6\sqrt{2} .\end{array} By combining like terms, the expression above is equivalent to \begin{array}{l}\require{cancel} (5-7+6)\sqrt{2} \\\\= 4\sqrt{2} .\end{array}