1. **State the problem:** We need to make $y$ the subject of the formula given by $$R = Z \sqrt{y^2 - x^2}.$$ 2. **Isolate the square root term:** Divide both sides by $Z$ to isolate the square root. $$\frac{R}{Z} = \sqrt{y^2 - x^2}.$$ 3. **Square both sides:** To remove the square root, square both sides of the equation. $$\left(\frac{R}{Z}\right)^2 = y^2 - x^2.$$ 4. **Rearrange to solve for $y^2$:** Add $x^2$ to both sides. $$y^2 = \left(\frac{R}{Z}\right)^2 + x^2.$$ 5. **Take the square root:** Finally, take the square root of both sides to solve for $y$. Remember to consider both positive and negative roots. $$y = \pm \sqrt{\left(\frac{R}{Z}\right)^2 + x^2}.$$ **Final answer:** $$y = \pm \sqrt{\left(\frac{R}{Z}\right)^2 + x^2}.$$