## Algebra: A Combined Approach (4th Edition)

$\dfrac{5}{\sqrt{27a}}=\dfrac{5\sqrt{3a}}{9a}$
$\dfrac{5}{\sqrt{27a}}$ Multiply the fraction by $\dfrac{\sqrt{27a}}{\sqrt{27a}}$: $\dfrac{5}{\sqrt{27a}}=\dfrac{5}{\sqrt{27a}}\cdot\dfrac{\sqrt{27a}}{\sqrt{27a}}=\dfrac{5\sqrt{27a}}{\sqrt{(27a)^{2}}}=\dfrac{5\sqrt{27a}}{27a}=...$ Rewrite the expression as $\dfrac{5\sqrt{9\cdot3\cdot a}}{27a}$ and simplify: $...=\dfrac{5(3)\sqrt{3a}}{27a}=\dfrac{5\sqrt{3a}}{9a}$