Question

(dfrac{3x^{3}y^{2}sqrt{2xy}}{4x^{2}ysqrt{5y}} =)

Explanation:

Step1: Simplify variable coefficients

$\frac{3}{4} \cdot \frac{x^3}{x^2} \cdot \frac{y^2}{y} \cdot \frac{\sqrt{2xy}}{\sqrt{5y}}$

Step2: Simplify monomial terms

$\frac{3}{4} \cdot x^{3-2} \cdot y^{2-1} \cdot \frac{\sqrt{2xy}}{\sqrt{5y}}$
$\frac{3}{4}xy \cdot \frac{\sqrt{2xy}}{\sqrt{5y}}$

Step3: Combine square roots

$\frac{3}{4}xy \cdot \sqrt{\frac{2xy}{5y}}$

Step4: Cancel $y$ in the root

$\frac{3}{4}xy \cdot \sqrt{\frac{2x}{5}}$

Step5: Rationalize the denominator

$\frac{3}{4}xy \cdot \frac{\sqrt{10x}}{5}$

Step6: Multiply constant terms

$\frac{3xy\sqrt{10x}}{20}$

Answer:

$\frac{3xy\sqrt{10x}}{20}$