If \(a=3+\sqrt{6}\) and \(b=3-\sqrt{6}\), what is the value of \(a+b\)?
Answer and explanation
Correct answer: 6
Add like terms: the rational parts 3 and 3 sum to 6, while the irrational parts \(+\sqrt{6}\) and \(-\sqrt{6}\) cancel. Therefore \(a+b=6\). Distractor D (\(6+2\sqrt{6}\)) is a common mistake resulting from adding the square-root terms instead of canceling them. Exam tip: look for conjugates — the ±√ terms cancel when summed, leaving twice the rational part.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Add like terms: the rational parts 3 and 3 sum to 6, while the irrational parts \(+\sqrt{6}\) and \(-\sqrt{6}\) cancel. Therefore \(a+b=6\). Distractor D (\(6+2\sqrt{6}\)) is a common mistake resulting from adding the square-root terms instead of canceling them. Exam tip: look for conjugates — the ±√ terms cancel when summed, leaving twice the rational part.
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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