problem: If $\sqrt{5x}\cdot\sqrt{10x}\cdot\sqrt{18x}=30$, find $x$.
solution: We begin by combining the radical expressions on the LHS of the equation, and expressing everything in terms of prime factors \begin{align*} \sqrt{5x}\cdot{\sqrt{10x}}\cdot{\sqrt{18x}}& =30
  \\\Rightarrow \qquad \sqrt{5\cdot{x}\cdot{5}\cdot{2}\cdot{x}\cdot{2}\cdot{3^2}\cdot{x}}& =30
  \\\Rightarrow \qquad \sqrt{5^2\cdot{2^2}\cdot{3^2}\cdot{x^3}}& =30
  \\\Rightarrow \qquad (5\cdot{2}\cdot{3})\sqrt{x^3}& =30
  \\\Rightarrow \qquad 30{x^{\frac32}}&=30
  \\\Rightarrow\qquad x^{\frac32}&=1
  \\\Rightarrow \qquad x&=\boxed{1}
  \end{align*}