Which of the following is the simplified form of \(\sqrt{162}\)?
Answer and explanation
Correct answer: \(9\sqrt{2}\)
\(\sqrt{162}=\sqrt{81\times2}=\sqrt{81}\cdot\sqrt{2}=9\sqrt{2}\). Therefore the correct simplified form is \(9\sqrt{2}\). Option B (\(6\sqrt{3}\)) is incorrect because \(6\sqrt{3}=\sqrt{36\times3}=\sqrt{108}\), which is not equal to \(\sqrt{162}\). Options C and D are also numerically different (\(18=\sqrt{324}\), and \(18\sqrt{2}\) is much larger). Exam tip: factor out the largest perfect square from under the root to simplify quickly.
Frequently asked questions
What is the correct answer to this question?
\(9\sqrt{2}\)
Why is this the correct answer?
\(\sqrt{162}=\sqrt{81\times2}=\sqrt{81}\cdot\sqrt{2}=9\sqrt{2}\). Therefore the correct simplified form is \(9\sqrt{2}\). Option B (\(6\sqrt{3}\)) is incorrect because \(6\sqrt{3}=\sqrt{36\times3}=\sqrt{108}\), which is not equal to \(\sqrt{162}\). Options C and D are also numerically different (\(18=\sqrt{324}\), and \(18\sqrt{2}\) is much larger). Exam tip: factor out the largest perfect square from under the root 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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