To simplify the expression \(9(7^{1/2}) + 3(7^{1/2})\), we first notice that both terms contain \(7^{1/2}\) (which is the square root of 7).
We can factor out \(7^{1/2}\):
\[ 9(7^{1/2}) + 3(7^{1/2}) = (9 + 3)(7^{1/2}) \]
Calculating \(9 + 3\):
\[ 9 + 3 = 12 \]
So we have:
\[ (9 + 3)(7^{1/2}) = 12(7^{1/2}) = 12\sqrt{7} \]
Looking back at the responses provided:
- 27 square root of 7
- 12 square root of 7
- 6 square root of 7
- 3 square root of 7
The correct answer is:
12 square root of 7 (or \(12\sqrt{7}\)).