1. The problem is to understand and simplify the expression $R = Z(\sqrt{y^2 + x^2})$. 2. This expression represents $R$ as the product of $Z$ and the square root of the sum of squares of $y$ and $x$. 3. The formula used here is the Pythagorean theorem inside the square root: $$\sqrt{y^2 + x^2}$$ which calculates the length of the hypotenuse of a right triangle with legs $x$ and $y$. 4. Multiplying by $Z$ scales this length by the factor $Z$. 5. There is no further simplification unless values for $Z$, $x$, and $y$ are given. 6. So, the expression $R = Z\sqrt{y^2 + x^2}$ is already in its simplest form.