What is the simplest form of \(\sqrt{27}+\sqrt{12}-\sqrt{3}\)?
Answer and explanation
Correct answer: \(4\sqrt{3}\)
Since \(27=9\times3\) and \(12=4\times3\), \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Thus, \(3\sqrt{3}+2\sqrt{3}-\sqrt{3}=4\sqrt{3}\). The distractor \(5\sqrt{3}\) results from forgetting to subtract the final \(\sqrt{3}\). Exam tip: extract perfect-square factors first, then combine like surds by adding or subtracting their coefficients.
Frequently asked questions
What is the correct answer to this question?
\(4\sqrt{3}\)
Why is this the correct answer?
Since \(27=9\times3\) and \(12=4\times3\), \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Thus, \(3\sqrt{3}+2\sqrt{3}-\sqrt{3}=4\sqrt{3}\). The distractor \(5\sqrt{3}\) results from forgetting to subtract the final \(\sqrt{3}\). Exam tip: extract perfect-square factors first, then combine like surds by adding or subtracting their coefficients.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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