Which of the following is the simplified form of \(\sqrt{245}\)?
Answer and explanation
Correct answer: \(7\sqrt{5}\)
Factor 245: \(245=49\times5\). Then \(\sqrt{245}=\sqrt{49\times5}=\sqrt{49}\times\sqrt{5}=7\sqrt{5}\), so A is correct. Option B (\(5\sqrt{7}\)) is incorrect — \((5\sqrt{7})^2=175\), not 245. Option C (\(49\sqrt{5}\)) arises from mistakenly taking 49 instead of its square root (\(\sqrt{49}=7\)), giving an answer that is far too large. Option D is just the unsimplified radical. Exam tip: always pull out the largest perfect square factor and take its square root outside the radical.
Frequently asked questions
What is the correct answer to this question?
\(7\sqrt{5}\)
Why is this the correct answer?
Factor 245: \(245=49\times5\). Then \(\sqrt{245}=\sqrt{49\times5}=\sqrt{49}\times\sqrt{5}=7\sqrt{5}\), so A is correct. Option B (\(5\sqrt{7}\)) is incorrect — \((5\sqrt{7})^2=175\), not 245. Option C (\(49\sqrt{5}\)) arises from mistakenly taking 49 instead of its square root (\(\sqrt{49}=7\)), giving an answer that is far too large. Option D is just the unsimplified radical. Exam tip: always pull out the largest perfect square factor and take its square root outside the radical.
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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