Algebra: A Combined Approach (4th Edition)

$\dfrac{\sqrt{3x^{5}}}{6}=\dfrac{x^{3}}{2\sqrt{3x}}$
$\dfrac{\sqrt{3x^{5}}}{6}$ First, simplify this expression: $\dfrac{\sqrt{3x^{5}}}{6}=\dfrac{x^{2}\sqrt{3x}}{6}=...$ Multiply this expression by $\dfrac{\sqrt{3x}}{\sqrt{3x}}$ and simplify again if possible: $...=\dfrac{x^{2}\sqrt{3x}}{6}\cdot\dfrac{\sqrt{3x}}{\sqrt{3x}}=\dfrac{x^{2}\sqrt{(3x)^{2}}}{6\sqrt{3x}}=\dfrac{x^{2}(3x)}{6\sqrt{3x}}=\dfrac{3x^{3}}{6\sqrt{3x}}=\dfrac{x^{3}}{2\sqrt{3x}}$