Which option gives the correct relation between \(\sqrt{3}\) and \(\sqrt{12}\)?
Answer and explanation
Correct answer: \(\sqrt{12}=2\sqrt{3}\)
Reason: \(\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}\). Hence option A is correct.
Why others are wrong: Option B (\(\sqrt{12}=4\sqrt{3}\)) and option C (\(\sqrt{12}=3\sqrt{2}\)) are incorrect because the largest perfect square factor of 12 is 4 (not 9 or 16), so only \(\sqrt{4}\) can be taken out. Option D yields a much smaller value and is clearly wrong.
Exam tip: To compare or simplify surds, factor the radicand and pull out the largest perfect square; this makes direct comparison trivial.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{12}=2\sqrt{3}\)
Why is this the correct answer?
Reason: \(\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}\). Hence option A is correct.
Why others are wrong: Option B (\(\sqrt{12}=4\sqrt{3}\)) and option C (\(\sqrt{12}=3\sqrt{2}\)) are incorrect because the largest perfect square factor of 12 is 4 (not 9 or 16), so only \(\sqrt{4}\) can be taken out. Option D yields a much smaller value and is clearly wrong.
Exam tip: To compare or simplify surds, factor the radicand and pull out the largest perfect square; this makes direct comparison trivial.
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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