Which option is the correct expansion of \((\sqrt{5}-\sqrt{2})^2\)?
Answer and explanation
Correct answer: \(7-2\sqrt{10}\)
Let \(a=\sqrt{5}\) and \(b=\sqrt{2}\). Using \((a-b)^2=a^2+b^2-2ab\) we get \((\sqrt{5}-\sqrt{2})^2=5+2-2\sqrt{10}=7-2\sqrt{10}\). So option A is correct. Option B misses the factor 2 in the cross term; option C has the wrong sign for the cross term; option D omits the cross term entirely. Exam tip: always apply the \(2ab\) term with the correct sign when expanding squares of binomials.
Frequently asked questions
What is the correct answer to this question?
\(7-2\sqrt{10}\)
Why is this the correct answer?
Let \(a=\sqrt{5}\) and \(b=\sqrt{2}\). Using \((a-b)^2=a^2+b^2-2ab\) we get \((\sqrt{5}-\sqrt{2})^2=5+2-2\sqrt{10}=7-2\sqrt{10}\). So option A is correct. Option B misses the factor 2 in the cross term; option C has the wrong sign for the cross term; option D omits the cross term entirely. Exam tip: always apply the \(2ab\) term with the correct sign when expanding squares of binomials.
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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