Which of the following is the correct expansion of \((3+\sqrt{2})^2\)?
Answer and explanation
Correct answer: \(11+6\sqrt{2}\)
Use the square identity \((a+b)^2=a^2+2ab+b^2\). With \(a=3\) and \(b=\sqrt{2}\) we get \((3+\sqrt{2})^2=3^2+2\cdot3\cdot\sqrt{2}+(\sqrt{2})^2=9+6\sqrt{2}+2=11+6\sqrt{2}\). Option B (\(9+6\sqrt{2}\)) omits the \(b^2\) term (+2) and is therefore incorrect. Exam tip: always write all three terms \(a^2,\;2ab,\;b^2\) when expanding a square of a binomial.
Frequently asked questions
What is the correct answer to this question?
\(11+6\sqrt{2}\)
Why is this the correct answer?
Use the square identity \((a+b)^2=a^2+2ab+b^2\). With \(a=3\) and \(b=\sqrt{2}\) we get \((3+\sqrt{2})^2=3^2+2\cdot3\cdot\sqrt{2}+(\sqrt{2})^2=9+6\sqrt{2}+2=11+6\sqrt{2}\). Option B (\(9+6\sqrt{2}\)) omits the \(b^2\) term (+2) and is therefore incorrect. Exam tip: always write all three terms \(a^2,\;2ab,\;b^2\) when expanding a square of a binomial.
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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