Which of the following is the value of \(\sqrt{5}(2+\sqrt{5})\)?
Answer and explanation
Correct answer: \(5+2\sqrt{5}\)
Multiply using distributive property: \(\sqrt{5}(2+\sqrt{5})=2\sqrt{5}+\sqrt{5}\cdot\sqrt{5}=2\sqrt{5}+5\). So the value is \(5+2\sqrt{5}\). Option B is close but has the wrong coefficient of \(\sqrt{5}\) (it shows \(1\sqrt{5}\) instead of \(2\sqrt{5}\)). Option C swaps the coefficients of the rational and irrational parts, and option D (1) is incorrect — that would arise only if numerator and denominator were identical or by an invalid cancellation. Exam tip: distribute the surd across each term and then combine like (rational and irrational) terms carefully.
Frequently asked questions
What is the correct answer to this question?
\(5+2\sqrt{5}\)
Why is this the correct answer?
Multiply using distributive property: \(\sqrt{5}(2+\sqrt{5})=2\sqrt{5}+\sqrt{5}\cdot\sqrt{5}=2\sqrt{5}+5\). So the value is \(5+2\sqrt{5}\). Option B is close but has the wrong coefficient of \(\sqrt{5}\) (it shows \(1\sqrt{5}\) instead of \(2\sqrt{5}\)). Option C swaps the coefficients of the rational and irrational parts, and option D (1) is incorrect — that would arise only if numerator and denominator were identical or by an invalid cancellation. Exam tip: distribute the surd across each term and then combine like (rational and irrational) terms carefully.
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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