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Section 1.3 : Radicals

13. Multiply the following expression. Assume that \(x\) is positive.

\[\sqrt x \left( {4 - 3\sqrt x } \right)\] Show Solution

All we need to do here is do the multiplication so here is that.

\[\sqrt x \left( {4 - 3\sqrt x } \right) = 4\sqrt x - 3\sqrt x \left( {\sqrt x } \right) = 4\sqrt x - 3\sqrt {{x^2}} = \require{bbox} \bbox[2pt,border:1px solid black]{{4\sqrt x - 3x}}\]

Don’t forget to simplify any resulting roots that can be. That is an often missed part of these problems.