I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.3 : Radicals
15. Multiply the following expression. Assume that \(x\) is positive.
\[\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)\] Show SolutionAll we need to do here is do the multiplication so here is that.
\[\begin{align*}\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right) & = 4\sqrt[3]{x} - \sqrt[3]{x}\,\,\sqrt[3]{{{x^2}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^2}}}\,\,\sqrt[3]{{{x^2}}}\\ & = 4\sqrt[3]{x} - \sqrt[3]{{{x^3}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^4}}}\\ & = 4\sqrt[3]{x} - \sqrt[3]{{{x^3}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^3}}}\,\,\sqrt[3]{x}\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{4\sqrt[3]{x} - x + 8\,\,\sqrt[3]{{{x^2}}} - 2x\,\,\sqrt[3]{x}}}\end{align*}\]Don’t forget to simplify any resulting roots that can be. That is an often missed part of these problems and when dealing with roots other than square roots there can be quite a bit of work in the simplification process as we saw with this problem.