Add the following radical expressions where \( a>0 \). \( \sqrt{81 a}+\sqrt{25 a}+\sqrt{4 a} \)

To add the radical expressions \( \sqrt{81 a}+\sqrt{25 a}+\sqrt{4 a} \), we first simplify each term individually: 1. \( \sqrt{81 a} = \sqrt{81} \cdot \sqrt{a} = 9\sqrt{a} \) 2. \( \sqrt{25 a} = \sqrt{25} \cdot \sqrt{a} = 5\sqrt{a} \) 3. \( \sqrt{4 a} = \sqrt{4} \cdot \sqrt{a} = 2\sqrt{a} \) Now we can add them together: \[ 9\sqrt{a} + 5\sqrt{a} + 2\sqrt{a} \] Combining like terms: \[ (9 + 5 + 2)\sqrt{a} = 16\sqrt{a} \] Thus, the final result is: \[ \sqrt{81 a} + \sqrt{25 a} + \sqrt{4 a} = 16\sqrt{a} \]