Combine the following expressions. \( \sqrt{16 a}-\sqrt{49 a}+\sqrt{81 a} \) \( 6 \sqrt{a} \) \( 4 a \sqrt{3} \) \( 4 \sqrt{3 a} \)

We start with the four expressions:   (1) √(16a) – √(49a) + √(81a)   (2) 6√a   (3) 4a√3   (4) 4√(3a) Step 1. Simplify Expression (1):   √(16a) = 4√a   √(49a) = 7√a   √(81a) = 9√a So,   4√a – 7√a + 9√a = (4 – 7 + 9)√a = 6√a Step 2. Write all expressions (after simplifying Expression (1)):   6√a  (from Expression 1)   6√a  (Expression 2)   4a√3  (Expression 3)   4√(3a)  (Expression 4) Notice that √(3a) can be written as √3 · √a, so Expression (4) becomes:   4√3√a Step 3. Combine all the terms:   6√a + 6√a = 12√a   Now add the remaining terms:   Total = 12√a + 4√3√a + 4a√3 We can factor √a from the first two terms if desired:   = √a (12 + 4√3) + 4a√3 or, factoring a 4:   = 4[√a(3 + √3) + a√3] This is the combined form of the original expressions. Thus, the final answer is:   (12 + 4√3)√a + 4a√3   or  4[√a(3 + √3) + a√3].