Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 41

$51$

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{3}+2\sqrt{6})(5\sqrt{3}-2\sqrt{6}) ,$ simplifies to \begin{array}{l}\require{cancel} (5\sqrt{3})^2-(2\sqrt{6})^2 \\\\= 25(3)-4(6) \\\\= 75-24 \\\\= 51 .\end{array}