If \(a=\sqrt{20}\), what is the simplified form of \(a\)?
Answer and explanation
Correct answer: \(2\sqrt{5}\)
\(\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}\). Pull out the largest perfect-square factor (here 4) from under the radical. Option B is not simplified (it’s the original form). Options C and D result from incorrect factor extraction. Exam tip: always factor the radicand and remove the largest perfect square to simplify quickly.
Frequently asked questions
What is the correct answer to this question?
\(2\sqrt{5}\)
Why is this the correct answer?
\(\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}\). Pull out the largest perfect-square factor (here 4) from under the radical. Option B is not simplified (it’s the original form). Options C and D result from incorrect factor extraction. Exam tip: always factor the radicand and remove the largest perfect square to simplify quickly.
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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