Which of the following is the correct expansion of \\((2+\sqrt{3})^2\\)?
Answer and explanation
Correct answer: 7+4\sqrt{3}
Use the square formula \\((a+b)^2=a^2+2ab+b^2\\). With \(a=2\) and \(b=\sqrt{3}\): \(a^2=4,\;2ab=4\sqrt{3},\;b^2=3\). Adding gives \(4+4\sqrt{3}+3=7+4\sqrt{3}\), so option A is correct. Option C (\(7+2\sqrt{3}\)) results from omitting the factor 2 in the middle term; option B (\(7\)) omits the middle term entirely; option D (\(4+4\sqrt{3}\)) omits the \(b^2\) term. Exam tip: compute each term \(a^2,\;2ab,\;b^2\) separately and optionally verify by approximating numerically.
Frequently asked questions
What is the correct answer to this question?
7+4\sqrt{3}
Why is this the correct answer?
Use the square formula \\((a+b)^2=a^2+2ab+b^2\\). With \(a=2\) and \(b=\sqrt{3}\): \(a^2=4,\;2ab=4\sqrt{3},\;b^2=3\). Adding gives \(4+4\sqrt{3}+3=7+4\sqrt{3}\), so option A is correct. Option C (\(7+2\sqrt{3}\)) results from omitting the factor 2 in the middle term; option B (\(7\)) omits the middle term entirely; option D (\(4+4\sqrt{3}\)) omits the \(b^2\) term. Exam tip: compute each term \(a^2,\;2ab,\;b^2\) separately and optionally verify by approximating numerically.
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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