text: ## Intermediate Algebra: Connecting Concepts through Application
  
  $-99+\sqrt 7$
  $(3+5\sqrt 7)(2-3\sqrt 7)$ =$3(2-3\sqrt 7)+5\sqrt 7(2-3\sqrt 7)$ =$6-9\sqrt 7+10\sqrt 7-3\sqrt 7(5\sqrt 7)$ =$6+(-9+10)\sqrt 7-(3\times5)(\sqrt 7\times\sqrt 7)$ =$6+1\sqrt 7-15(7)$ =$6+\sqrt 7-105$ =$6-105+\sqrt 7$ =$-99+\sqrt 7$