# Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 660: 33

$3\sqrt{30}-3\sqrt{35}$

#### Work Step by Step

Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 3\sqrt{5}(\sqrt{6}-\sqrt{7}) \\\\= 3\sqrt{5}(\sqrt{6})+3\sqrt{5}(-\sqrt{7}) .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} 3\sqrt{5(6)}-3\sqrt{5(7)} \\\\= 3\sqrt{30}-3\sqrt{35} .\end{array}

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