What is the simplified form of \(\sqrt{32}\)?
Answer and explanation
Correct answer: \(4\sqrt{2}\)
\(\sqrt{32}=\sqrt{16\times2}=\sqrt{16}\cdot\sqrt{2}=4\sqrt{2}\). Hence the simplified form is \(4\sqrt{2}\). Option B (\(8\sqrt{2}\)) is much larger and incorrect; option C (\(4\)) equals \(\sqrt{16}\), not \(\sqrt{32}\); option D is the unsimplified radical. Exam tip: always factor out the largest perfect square from under the root.
Frequently asked questions
What is the correct answer to this question?
\(4\sqrt{2}\)
Why is this the correct answer?
\(\sqrt{32}=\sqrt{16\times2}=\sqrt{16}\cdot\sqrt{2}=4\sqrt{2}\). Hence the simplified form is \(4\sqrt{2}\). Option B (\(8\sqrt{2}\)) is much larger and incorrect; option C (\(4\)) equals \(\sqrt{16}\), not \(\sqrt{32}\); option D is the unsimplified radical. Exam tip: always factor out the largest perfect square from under the root.
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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