Question

For each of the fractions below, rationalize the denominator and reduce any fractions if possible. Enter a fraction (perhaps involving a square root in the numerator), and not a decimal value.1/√19=5/√105/√5=

Answer 1

To rationalize the denominator, we would multiply each fraction by a numerator and denominator that is the same as the denominator of the original fraction. Thus we have

$\begin{gathered} 1)\frac{1}{\sqrt[]{19}}\times\frac{\sqrt[]{19}}{\sqrt[]{19}} \\ =\text{ }\frac{\sqrt[]{19}}{19} \\ 2)\text{ }\frac{5}{\sqrt[]{10}}\times\frac{\sqrt[]{10}}{\sqrt[]{10}} \\ =\text{ }\frac{5\sqrt[]{10}}{10}\text{ = }\frac{\sqrt[]{10}}{2} \\ 3)\text{ }\frac{5}{\sqrt[]{5}}\times\frac{\sqrt[]{5}}{\sqrt[]{5}} \\ =\text{ }\frac{5\sqrt[]{5}}{5} \\ =\text{ }\sqrt[]{5} \\ \end{gathered}$