1. **Statement of the problem:** Simplify the expression $$A = 5\sqrt{28} + \sqrt{7} - 3\sqrt{63}$$. 2. **Recall the rule:** Simplify square roots by factoring out perfect squares: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. 3. **Simplify each term:** - $$5\sqrt{28} = 5\sqrt{4 \times 7} = 5 \times \sqrt{4} \times \sqrt{7} = 5 \times 2 \times \sqrt{7} = 10\sqrt{7}$$ - $$\sqrt{7}$$ stays as is. - $$3\sqrt{63} = 3\sqrt{9 \times 7} = 3 \times \sqrt{9} \times \sqrt{7} = 3 \times 3 \times \sqrt{7} = 9\sqrt{7}$$ 4. **Rewrite the expression:** $$A = 10\sqrt{7} + \sqrt{7} - 9\sqrt{7}$$ 5. **Combine like terms:** $$A = (10 + 1 - 9)\sqrt{7} = 2\sqrt{7}$$ **Final answer:** $$A = 2\sqrt{7}$$