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What is the simplest form of \((\sqrt{32}+\sqrt{18})\)?
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Answer and explanation
Correct answer: \(7\sqrt{2}\)
\(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\) and \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Therefore, \(\sqrt{32}+\sqrt{18}=4\sqrt{2}+3\sqrt{2}=7\sqrt{2}\), so option B is correct. Exam tip: Factor out the largest perfect-square factor before adding surds.
Frequently asked questions
What is the correct answer to this question?
\(7\sqrt{2}\)
Why is this the correct answer?
\(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\) and \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Therefore, \(\sqrt{32}+\sqrt{18}=4\sqrt{2}+3\sqrt{2}=7\sqrt{2}\), so option B is correct. Exam tip: Factor out the largest perfect-square factor before adding surds.
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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