1. **State the problem:** Simplify the expression $$A= \sqrt{52 a^2 + 14 a \sqrt{3} a^2}$$. 2. **Rewrite the expression inside the square root:** $$52 a^2 + 14 a \sqrt{3} a^2 = 52 a^2 + 14 a^3 \sqrt{3}$$ 3. **Factor out the common term:** The common factor is $$a^2$$, so: $$a^2 (52 + 14 a \sqrt{3})$$ 4. **Use the property of square roots:** $$\sqrt{a^2 (52 + 14 a \sqrt{3})} = |a| \sqrt{52 + 14 a \sqrt{3}}$$ 5. **Final simplified form:** $$A = |a| \sqrt{52 + 14 a \sqrt{3}}$$ This is the simplest exact form unless further information about $$a$$ is given.