1. **State the problem:** We have a right triangle with one leg of length 11 and hypotenuse of length $x$. We need to find the length of the other leg in simplest radical form with a rational denominator. 2. **Use the Pythagorean theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relation is $$a^2 + b^2 = c^2$$ 3. **Assign known values:** Let the unknown leg be $b$, the known leg be 11, and the hypotenuse be $x$. Then: $$11^2 + b^2 = x^2$$ 4. **Solve for $b^2$:** $$b^2 = x^2 - 11^2 = x^2 - 121$$ 5. **Express $b$:** $$b = \sqrt{x^2 - 121}$$ 6. **Simplify radical if possible:** Since $x$ is the hypotenuse and must be greater than 11, the expression is valid. The radical is already in simplest form. 7. **Rationalize denominator if needed:** Here, $b$ is expressed as a radical with no denominator, so it is already rationalized. **Final answer:** $$b = \sqrt{x^2 - 121}$$