Which of the following is the value of \(\sqrt{3}(4+\sqrt{3})\)?
Answer and explanation
Correct answer: \(3+4\sqrt{3}\)
Distribute: \(\sqrt{3}(4+\sqrt{3})=4\sqrt{3}+\sqrt{3}\cdot\sqrt{3}=4\sqrt{3}+3\). So the simplified form is \(3+4\sqrt{3}\). Option (B) swaps the rational and irrational coefficients and is therefore incorrect; (C) and (D) are pure surd forms that would result from mistaken addition or multiplication of terms. Exam tip: multiply each term separately, simplify \(\sqrt{a}\cdot\sqrt{a}=a\), then combine rational and irrational parts.
Frequently asked questions
What is the correct answer to this question?
\(3+4\sqrt{3}\)
Why is this the correct answer?
Distribute: \(\sqrt{3}(4+\sqrt{3})=4\sqrt{3}+\sqrt{3}\cdot\sqrt{3}=4\sqrt{3}+3\). So the simplified form is \(3+4\sqrt{3}\). Option (B) swaps the rational and irrational coefficients and is therefore incorrect; (C) and (D) are pure surd forms that would result from mistaken addition or multiplication of terms. Exam tip: multiply each term separately, simplify \(\sqrt{a}\cdot\sqrt{a}=a\), then combine rational and irrational parts.
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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