\(\sqrt{75}-\sqrt{27}+\sqrt{12}\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(4\sqrt{3}\)
Square roots can be added or subtracted only when they are like surds. Take the largest perfect square out of each number to bring all three to \(\sqrt{3}\).
\(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\)
\(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\)
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\)
\(5\sqrt{3}-3\sqrt{3}+2\sqrt{3}=4\sqrt{3}\)