If \(x=\sqrt{7}-\sqrt{3}\), what is \(x^2\)?
Answer and explanation
Correct answer: 10-2\sqrt{21}
Use the identity \((a-b)^2=a^2+b^2-2ab)\). With \(a=\sqrt{7},\; b=\sqrt{3}\) we get \(x^2=(\sqrt{7}-\sqrt{3})^2=7+3-2\sqrt{21}=10-2\sqrt{21}\). Option B (\(10+2\sqrt{21}\)) is the typical sign-error from treating the cross term as positive. Exam tip: always expand using the identity and check the sign of the \(2ab\) term.
Frequently asked questions
What is the correct answer to this question?
10-2\sqrt{21}
Why is this the correct answer?
Use the identity \((a-b)^2=a^2+b^2-2ab)\). With \(a=\sqrt{7},\; b=\sqrt{3}\) we get \(x^2=(\sqrt{7}-\sqrt{3})^2=7+3-2\sqrt{21}=10-2\sqrt{21}\). Option B (\(10+2\sqrt{21}\)) is the typical sign-error from treating the cross term as positive. Exam tip: always expand using the identity and check the sign of the \(2ab\) term.
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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