1. **Problem statement:** We have an isosceles right triangle with two equal sides of length $x$ and a base of length 3. We need to find $x$ in simplest radical form with a rational denominator. 2. **Key fact:** In an isosceles right triangle, the legs are equal and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Identify sides:** Since the base is 3 and the triangle is isosceles with two equal sides $x$, the base must be the hypotenuse (the side opposite the right angle). 4. **Use the formula:** Hypotenuse $= x\sqrt{2}$, so $$3 = x\sqrt{2}$$ 5. **Solve for $x$:** $$x = \frac{3}{\sqrt{2}}$$ 6. **Rationalize the denominator:** $$x = \frac{3}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2}$$ 7. **Final answer:** $$x = \frac{3\sqrt{2}}{2}$$ This is the length of each equal side in simplest radical form with a rational denominator.