1. **State the problem:** Solve for $x$ in the equation $\sqrt{3x} = 15$. 2. **Formula and rules:** To solve for $x$, we need to eliminate the square root by squaring both sides of the equation. Remember, squaring both sides is valid but be careful to check for extraneous solutions if needed. 3. **Square both sides:** $$\left(\sqrt{3x}\right)^2 = 15^2$$ $$3x = 225$$ 4. **Isolate $x$:** $$x = \frac{225}{3}$$ 5. **Simplify the fraction:** $$x = \cancel{\frac{225}{\cancel{3}}} = 75$$ 6. **Final answer:** $$x = 75$$ This means the value of $x$ that satisfies the equation $\sqrt{3x} = 15$ is $75$.