Simplify: \(\sqrt{108} + \sqrt{125} - \sqrt{75}\)
A
\(\sqrt{3} + 5\sqrt{5}\)
B
\(6 \sqrt{3} - 5 \sqrt{5}\)
C
\(6 \sqrt{3} + \sqrt{2}\)
D
\(6\sqrt{3} - \sqrt{2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\sqrt{108} + \sqrt{125} - \sqrt{75}\)
= \(\sqrt{3 \times 36} + \sqrt{5 \times 25} - \sqrt{3 \times 25}\)
= \(6 \sqrt{3} + 5 \sqrt{5} - 5 \sqrt{3}\)
= \(\sqrt{3} + 5\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #49030)