Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 45

$1$

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, $ (2-\sqrt{3})(2+\sqrt{3}) ,$ is equivalent to \begin{array}{l}\require{cancel} 2^2-(\sqrt{3})^2 \\\\= 4-3 \\\\= 1 .\end{array}