1. **State the problem:** We have a right triangle with a hypotenuse of length 7 inches and one leg of length 4 inches. We need to find the length of the other leg in simplest radical form. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse and $a$, $b$ are the legs. 3. **Assign values:** Let the unknown leg be $x$. Then: $$4^2 + x^2 = 7^2$$ 4. **Calculate squares:** $$16 + x^2 = 49$$ 5. **Isolate $x^2$:** $$x^2 = 49 - 16$$ $$x^2 = 33$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{33}$$ 7. **Simplify radical:** 33 factors as $3 \times 11$, both prime, so $\sqrt{33}$ is already in simplest radical form. **Final answer:** The length of the other leg is $\sqrt{33}$ inches.