Which of the following is the value of \( (\sqrt{3}+\sqrt{12})^2 \)?
Answer and explanation
Correct answer: 27
Since \(\sqrt{12}=2\sqrt{3}\), we have \(\sqrt{3}+\sqrt{12}=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\). Squaring gives \((3\sqrt{3})^2=9\cdot(\sqrt{3})^2=9\cdot3=27\). Choice B (\(9\sqrt{3}\)) is a common mistake: squaring the expression gives a numeric product, not another radical of the same form. Exam tip: combine like surds first, then apply \((a\sqrt{b})^2=a^2b\).
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Since \(\sqrt{12}=2\sqrt{3}\), we have \(\sqrt{3}+\sqrt{12}=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\). Squaring gives \((3\sqrt{3})^2=9\cdot(\sqrt{3})^2=9\cdot3=27\). Choice B (\(9\sqrt{3}\)) is a common mistake: squaring the expression gives a numeric product, not another radical of the same form. Exam tip: combine like surds first, then apply \((a\sqrt{b})^2=a^2b\).
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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