What is the simplest form of \((\sqrt{5}+\sqrt{20})\)?
Answer and explanation
Correct answer: \(3\sqrt{5}\)
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Therefore, \(\sqrt{5}+\sqrt{20}=\sqrt{5}+2\sqrt{5}=3\sqrt{5}\). Option C is only the simplified form of \(\sqrt{20}\) and omits the original \(\sqrt{5}\). Exam tip: add the coefficients of like surd terms, using \(a\sqrt{b}+c\sqrt{b}=(a+c)\sqrt{b}\).
Frequently asked questions
What is the correct answer to this question?
\(3\sqrt{5}\)
Why is this the correct answer?
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Therefore, \(\sqrt{5}+\sqrt{20}=\sqrt{5}+2\sqrt{5}=3\sqrt{5}\). Option C is only the simplified form of \(\sqrt{20}\) and omits the original \(\sqrt{5}\). Exam tip: add the coefficients of like surd terms, using \(a\sqrt{b}+c\sqrt{b}=(a+c)\sqrt{b}\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Real Numbers.
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