Which is the simplest form of (\sqrt{80}) for understanding its position on the number line?
Answer and explanation
Correct answer: \(4\sqrt{5}\)
Since \(80=16\times5\) and 16 is the largest perfect-square factor of 80, \(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\). Option B, \(2\sqrt{20}\), is equivalent but not in simplest form. Also, \(4\sqrt{5}\approx8.94\), so the number lies between 8 and 9 on the number line. Exam tip: when simplifying a square root, extract the largest perfect-square factor.
Frequently asked questions
What is the correct answer to this question?
\(4\sqrt{5}\)
Why is this the correct answer?
Since \(80=16\times5\) and 16 is the largest perfect-square factor of 80, \(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\). Option B, \(2\sqrt{20}\), is equivalent but not in simplest form. Also, \(4\sqrt{5}\approx8.94\), so the number lies between 8 and 9 on the number line. Exam tip: when simplifying a square root, extract the largest perfect-square factor.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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