Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 47

$-5$

Using $(a+b)(a-b)=a^2-b^2$, or the product of the sum and difference of like terms, and the properties of radicals, the given expression, $ (\sqrt{10}-\sqrt{15})(\sqrt{10}+\sqrt{15}) ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{10})^2-(\sqrt{15})^2 \\\\= 10-15 \\\\= -5 .\end{array}