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\(\sqrt{15}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
3 \(\sqrt{45} - 12\sqrt{5} + 16\sqrt{20}\)
= 3 x \(\sqrt{9 \times 5} - 12 \times \sqrt{5} + 16 \times \sqrt{4 \times 5}\)
= 3 x 3 x \(\sqrt{5} - 12 \times \sqrt{5} + 16 \times 2 \times \sqrt{5}\)
= 9\(\sqrt{5} - 2 \sqrt{5} + 32 \sqrt{5}\)
= 9\(\sqrt{5} + 32\sqrt{5} - 12\sqrt{5}\)
= 29\(\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #36233)