1. **State the problem:** We are given the equation $x = 3\sqrt{\frac{y}{p}}$ and want to understand or manipulate it. 2. **Recall the formula and rules:** The square root function $\sqrt{\cdot}$ means raising to the power $\frac{1}{2}$. The expression inside the root is a fraction $\frac{y}{p}$. 3. **Rewrite the equation:** We can write the square root as an exponent: $$x = 3\left(\frac{y}{p}\right)^{\frac{1}{2}}$$ 4. **Isolate the root term:** Divide both sides by 3: $$\frac{x}{3} = \left(\frac{y}{p}\right)^{\frac{1}{2}}$$ 5. **Show cancellation explicitly:** $$\frac{\cancel{x}}{\cancel{3}} = \left(\frac{y}{p}\right)^{\frac{1}{2}}$$ 6. **Square both sides to remove the root:** $$\left(\frac{x}{3}\right)^2 = \frac{y}{p}$$ 7. **Simplify the left side:** $$\frac{x^2}{9} = \frac{y}{p}$$ 8. **Solve for $y$ by multiplying both sides by $p$:** $$y = p \cdot \frac{x^2}{9} = \frac{p x^2}{9}$$ **Final answer:** $$y = \frac{p x^2}{9}$$ This shows how to express $y$ in terms of $x$ and $p$ from the original equation.