Simplify \(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\)leaving your answer in surd form
A
\(29\sqrt{5}\)
B
\(14\sqrt{15}\)
C
\(12\sqrt{15}\)
D
\(11\sqrt{5}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\)
3\(\sqrt{5\times 9}-12\sqrt{5}+16\sqrt{4\times 5}\)
3\(\times 3\sqrt{5}-12\sqrt{5}+16\times 2\sqrt{5}\)
9\(\sqrt{5}-12\sqrt{5}+32\sqrt{5}\)
29\(\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #26721)