Which option is the value of \((\sqrt{13}-\sqrt{3})(\sqrt{13}+\sqrt{3})\)?
Answer and explanation
Correct answer: 10
Use the identity \((a-b)(a+b)=a^2-b^2\). With \(a=\sqrt{13}\) and \(b=\sqrt{3}\) we get \(13-3=10\), so the value is 10. Option C (\(\sqrt{39}\)) confuses the product of the individual square roots with the whole conjugate product; \(\sqrt{13}\cdot\sqrt{3}=\sqrt{39}\) is not equal to \((\sqrt{13}-\sqrt{3})(\sqrt{13}+\sqrt{3})\). Exam tip: spot the conjugate pair and apply the difference-of-squares formula to simplify quickly.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Use the identity \((a-b)(a+b)=a^2-b^2\). With \(a=\sqrt{13}\) and \(b=\sqrt{3}\) we get \(13-3=10\), so the value is 10. Option C (\(\sqrt{39}\)) confuses the product of the individual square roots with the whole conjugate product; \(\sqrt{13}\cdot\sqrt{3}=\sqrt{39}\) is not equal to \((\sqrt{13}-\sqrt{3})(\sqrt{13}+\sqrt{3})\). Exam tip: spot the conjugate pair and apply the difference-of-squares formula to simplify quickly.
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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