Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 32

$31+11\sqrt[]{3}$

Using the FOIL method and the properties of radicals, the given expression, $ (\sqrt[]{3}+4)(\sqrt[]{3}+7) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{3}(\sqrt[]{3})+\sqrt[]{3}(7)+4(\sqrt[]{3})+4(7) \\\\= 3+7\sqrt[]{3}+4\sqrt[]{3}+28 \\\\= (3+28)+(7\sqrt[]{3}+4\sqrt[]{3}) \\\\= 31+11\sqrt[]{3} .\end{array}