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\(\sqrt{15}\)
Correct Answer: A
Explanation
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\(\sqrt{5}\)
