1. The problem asks to simplify the expression $$(3+2\sqrt{7})^2$$. 2. Use the formula for squaring a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$. 3. Identify $a = 3$$ and $$b = 2\sqrt{7}$$. 4. Calculate each term: - $$a^2 = 3^2 = 9$$ - $$2ab = 2 \times 3 \times 2\sqrt{7} = 12\sqrt{7}$$ - $$b^2 = (2\sqrt{7})^2 = 4 \times 7 = 28$$ 5. Combine all terms: $$9 + 12\sqrt{7} + 28 = 37 + 12\sqrt{7}$$ So, the simplified form of $$(3+2\sqrt{7})^2$$ is $$37 + 12\sqrt{7}$$.