Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.3 : Radicals
18. Rationalize the denominator. Assume that \(x\) and \(y\) are positive.
\[\frac{4}{{\sqrt x + 2\sqrt y }}\] Show SolutionFor this problem we need to multiply the numerator and denominator by \(\sqrt x - 2\sqrt y \) in order to rationalize the denominator.
\[\frac{4}{{\sqrt x + 2\sqrt y }} = \frac{4}{{\sqrt x + 2\sqrt y }}\frac{{\sqrt x - 2\sqrt y }}{{\sqrt x - 2\sqrt y }} = \frac{{4\left( {\sqrt x - 2\sqrt y } \right)}}{{\left( {\sqrt x + 2\sqrt y } \right)\left( {\sqrt x - 2\sqrt y } \right)}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{4\sqrt x - 8\sqrt y }}{{x - 4y}}}}\]