1. **State the problem:** Rationalize the denominator of the expression $$\frac{\sqrt{10}}{3\sqrt{2}}$$. 2. **Recall the rule:** To rationalize a denominator containing a square root, multiply numerator and denominator by the conjugate or the radical itself to eliminate the square root in the denominator. 3. **Apply the rule:** Multiply numerator and denominator by $$\sqrt{2}$$: $$\frac{\sqrt{10}}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{10} \times \sqrt{2}}{3 \times \sqrt{2} \times \sqrt{2}}$$ 4. **Simplify the numerator:** $$\sqrt{10} \times \sqrt{2} = \sqrt{10 \times 2} = \sqrt{20}$$ 5. **Simplify the denominator:** $$3 \times \sqrt{2} \times \sqrt{2} = 3 \times 2 = 6$$ 6. **Simplify $$\sqrt{20}$$:** $$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$$ 7. **Write the final simplified expression:** $$\frac{2\sqrt{5}}{6} = \frac{\sqrt{5}}{3}$$ **Answer:** $$\frac{\sqrt{5}}{3}$$