What is the simplified form of \((\sqrt{2}+\sqrt{8}+\sqrt{18})\)?
Answer and explanation
Correct answer: \(6\sqrt{2}\)
Simplify each radical first: \(\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}\) and \(\sqrt{18}=\sqrt{9\cdot2}=3\sqrt{2}\). Combine like terms: \(\sqrt{2}+2\sqrt{2}+3\sqrt{2}=(1+2+3)\sqrt{2}=6\sqrt{2}\). Thus the correct answer is \(6\sqrt{2}\). A common wrong choice (e.g. \(4\sqrt{2}\)) comes from mis‑simplifying \(\sqrt{18}\) as \(2\sqrt{2}\); remember \(\sqrt{18}=3\sqrt{2}\). Exam tip: always simplify radicals to the same radicand before adding or subtracting.
Frequently asked questions
What is the correct answer to this question?
\(6\sqrt{2}\)
Why is this the correct answer?
Simplify each radical first: \(\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}\) and \(\sqrt{18}=\sqrt{9\cdot2}=3\sqrt{2}\). Combine like terms: \(\sqrt{2}+2\sqrt{2}+3\sqrt{2}=(1+2+3)\sqrt{2}=6\sqrt{2}\). Thus the correct answer is \(6\sqrt{2}\). A common wrong choice (e.g. \(4\sqrt{2}\)) comes from mis‑simplifying \(\sqrt{18}\) as \(2\sqrt{2}\); remember \(\sqrt{18}=3\sqrt{2}\). Exam tip: always simplify radicals to the same radicand before adding or subtracting.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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