Which of the following is the value of \((\sqrt{7}+1)(\sqrt{7}-1)\)?
Answer and explanation
Correct answer: 6
Use the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\). With \(a=\sqrt{7}\) and \(b=1\) we get \(7-1=6\), so A is correct. Option B (8) is a common mistake from adding \(7+1\) instead of subtracting. Options C and D are different expressions and do not equal 6. Exam tip: spot the pattern \((a+b)(a-b)\) and apply \(a^2-b^2\) immediately to avoid arithmetic mistakes.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Use the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\). With \(a=\sqrt{7}\) and \(b=1\) we get \(7-1=6\), so A is correct. Option B (8) is a common mistake from adding \(7+1\) instead of subtracting. Options C and D are different expressions and do not equal 6. Exam tip: spot the pattern \((a+b)(a-b)\) and apply \(a^2-b^2\) immediately to avoid arithmetic mistakes.
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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