# Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 52

$21+4\sqrt{x}-x$

#### Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the FOIL method, and the properties of radicals, the given expression, $(3+\sqrt{x})(7-\sqrt{x}) ,$ simplifies to \begin{array}{l}\require{cancel} 3(7)+3(-\sqrt{x})+\sqrt{x}(7)+\sqrt{x}(-\sqrt{x}) \\\\= 21-3\sqrt{x}+7\sqrt{x}-x \\\\= 21+4\sqrt{x}-x .\end{array} Note that all variables represent positive real numbers.

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