Which of the following is the simplified form of \(\sqrt{180}\)?
Answer and explanation
Correct answer: \(6\sqrt{5}\)
\(\sqrt{180}=\sqrt{36\times5}=\sqrt{36}\,\sqrt{5}=6\sqrt{5}\), so the simplified form is \(6\sqrt{5}\). Why other options are wrong: \(9\sqrt{2}\) squared is \(81\times2=162\) (not 180), \(5\sqrt{6}\) squared is \(25\times6=150\), and \(3\sqrt{12}=3\sqrt{4\times3}=6\sqrt{3}\), which is different from \(6\sqrt{5}\). Exam tip: always factor out the largest perfect square from under the radical to simplify quickly.
Frequently asked questions
What is the correct answer to this question?
\(6\sqrt{5}\)
Why is this the correct answer?
\(\sqrt{180}=\sqrt{36\times5}=\sqrt{36}\,\sqrt{5}=6\sqrt{5}\), so the simplified form is \(6\sqrt{5}\). Why other options are wrong: \(9\sqrt{2}\) squared is \(81\times2=162\) (not 180), \(5\sqrt{6}\) squared is \(25\times6=150\), and \(3\sqrt{12}=3\sqrt{4\times3}=6\sqrt{3}\), which is different from \(6\sqrt{5}\). Exam tip: always factor out the largest perfect square from under the radical 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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