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What is the simplified form of \(\sqrt{75}\)?
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Answer and explanation
Correct answer: \(5\sqrt{3}\)
Since \(75=25\times3\), and \(25\) is a perfect square, \(\sqrt{75}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}\). \(3\sqrt{5}\) is incorrect because \((3\sqrt{5})^2=45\), not 75. Exam tip: To simplify a surd, identify and factor out the greatest perfect-square factor.
Frequently asked questions
What is the correct answer to this question?
\(5\sqrt{3}\)
Why is this the correct answer?
Since \(75=25\times3\), and \(25\) is a perfect square, \(\sqrt{75}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}\). \(3\sqrt{5}\) is incorrect because \((3\sqrt{5})^2=45\), not 75. Exam tip: To simplify a surd, identify and factor out the greatest perfect-square factor.
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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