Which is the simplest radical form of \(\sqrt{180}\) for locating it on the number line?
Answer and explanation
Correct answer: \(6\sqrt{5}\)
Since \(180=36\times5\) and \(36\) is the largest perfect-square factor, \(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\). Option A, \(3\sqrt{20}\), is equivalent but not fully simplified because \(20\) still contains the square factor \(4\). For such questions, take the largest perfect-square factor outside the radical.
Frequently asked questions
What is the correct answer to this question?
\(6\sqrt{5}\)
Why is this the correct answer?
Since \(180=36\times5\) and \(36\) is the largest perfect-square factor, \(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\). Option A, \(3\sqrt{20}\), is equivalent but not fully simplified because \(20\) still contains the square factor \(4\). For such questions, take the largest perfect-square factor outside the radical.
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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