1. **State the problem:** Simplify the expression $$(\sqrt{2} - \sqrt{3})^2$$. 2. **Recall the formula:** The square of a binomial $(a - b)^2$ is given by $$a^2 - 2ab + b^2$$. 3. **Apply the formula:** Here, $a = \sqrt{2}$ and $b = \sqrt{3}$. $$ (\sqrt{2} - \sqrt{3})^2 = (\sqrt{2})^2 - 2 \times \sqrt{2} \times \sqrt{3} + (\sqrt{3})^2 $$ 4. **Calculate each term:** - $(\sqrt{2})^2 = 2$ - $2 \times \sqrt{2} \times \sqrt{3} = 2 \times \sqrt{6} = 2\sqrt{6}$ - $(\sqrt{3})^2 = 3$ 5. **Substitute back:** $$ 2 - 2\sqrt{6} + 3 $$ 6. **Combine like terms:** $$ 5 - 2\sqrt{6} $$ **Final answer:** $$ (\sqrt{2} - \sqrt{3})^2 = 5 - 2\sqrt{6} $$