Which of the following is the value of \(4\sqrt{3}-\sqrt{27}\)?
Answer and explanation
Correct answer: \(\sqrt{3}\)
Simplify first: \(\sqrt{27}=\sqrt{9\cdot3}=3\sqrt{3}\). Thus \(4\sqrt{3}-\sqrt{27}=4\sqrt{3}-3\sqrt{3}=\sqrt{3}\), so option A is correct. Option B (1) is wrong because \(\sqrt{3}\approx1.732\), not 1. Option C (\(3\sqrt{3}\)) is incorrect because it treats the second term as if it should be added or left unsimplified; the correct simplification gives subtraction of like terms. Exam tip: always simplify radicals first and then combine only like surd terms (same radical part).
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{3}\)
Why is this the correct answer?
Simplify first: \(\sqrt{27}=\sqrt{9\cdot3}=3\sqrt{3}\). Thus \(4\sqrt{3}-\sqrt{27}=4\sqrt{3}-3\sqrt{3}=\sqrt{3}\), so option A is correct. Option B (1) is wrong because \(\sqrt{3}\approx1.732\), not 1. Option C (\(3\sqrt{3}\)) is incorrect because it treats the second term as if it should be added or left unsimplified; the correct simplification gives subtraction of like terms. Exam tip: always simplify radicals first and then combine only like surd terms (same radical part).
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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