If x = \sqrt{6} + \sqrt{2}, what is the value of x^2?
Answer and explanation
Correct answer: 8+4\sqrt{3}
Expand the square: x^2 = (\sqrt{6}+\sqrt{2})^2 = 6 + 2 + 2\sqrt{12} = 8 + 2\times 2\sqrt{3} = 8 + 4\sqrt{3}. Option B (8+2\sqrt{3}) is a common error caused by not fully simplifying \sqrt{12} (since \sqrt{12}=2\sqrt{3}, the cross-term becomes 4\sqrt{3}, not 2\sqrt{3}). Exam tip: apply (a+b)^2 = a^2+2ab+b^2 and simplify radicals fully before choosing the answer.
Frequently asked questions
What is the correct answer to this question?
8+4\sqrt{3}
Why is this the correct answer?
Expand the square: x^2 = (\sqrt{6}+\sqrt{2})^2 = 6 + 2 + 2\sqrt{12} = 8 + 2\times 2\sqrt{3} = 8 + 4\sqrt{3}. Option B (8+2\sqrt{3}) is a common error caused by not fully simplifying \sqrt{12} (since \sqrt{12}=2\sqrt{3}, the cross-term becomes 4\sqrt{3}, not 2\sqrt{3}). Exam tip: apply (a+b)^2 = a^2+2ab+b^2 and simplify radicals fully before choosing the answer.
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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