Section 1.3 : Radicals
14. Multiply the following expression. Assume that \(x\) is positive.
\[\left( {2\sqrt x + 1} \right)\left( {3 - 4\sqrt x } \right)\] Show SolutionAll we need to do here is do the multiplication so here is that.
\[\left( {2\sqrt x + 1} \right)\left( {3 - 4\sqrt x } \right) = 6\sqrt x - 8\sqrt x \left( {\sqrt x } \right) + 3 - 4\sqrt x = 3 + 2\sqrt x - 8\sqrt {{x^2}} = \require{bbox} \bbox[2pt,border:1px solid black]{{3 + 2\sqrt x - 8x}}\]Don’t forget to simplify any resulting roots that can be. That is an often missed part of these problems.