Which option gives the simplified form of \(\sqrt{147}\)?
Answer and explanation
Correct answer: \(7\sqrt{3}\)
\(\sqrt{147}=\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}=7\sqrt{3}\). Thus the simplified form is \(7\sqrt{3}\). Option B is incorrect because \(3\sqrt{7}\) would arise from \(\sqrt{9\times7}\), which is not the factorization here. Option C is just the unsimplified radical and D is three times the correct value. Exam tip: always factor the radicand to find the largest perfect square and take its square root outside the radical (here 49 → 7).
Frequently asked questions
What is the correct answer to this question?
\(7\sqrt{3}\)
Why is this the correct answer?
\(\sqrt{147}=\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}=7\sqrt{3}\). Thus the simplified form is \(7\sqrt{3}\). Option B is incorrect because \(3\sqrt{7}\) would arise from \(\sqrt{9\times7}\), which is not the factorization here. Option C is just the unsimplified radical and D is three times the correct value. Exam tip: always factor the radicand to find the largest perfect square and take its square root outside the radical (here 49 → 7).
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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