Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 40

$148$

Using $(a+b)(a-b)=a^2-b^2$, or the special product of the sum and difference of like terms, the given expression, $ (5\sqrt{6}-\sqrt{2})(5\sqrt{6}+\sqrt{2}) ,$ simplifies to \begin{array}{l}\require{cancel} (5\sqrt{6})^2-(\sqrt{2})^2 \\\\= 25(6)-2 \\\\= 150-2 \\\\= 148 .\end{array}