Which of the following gives the correct value of \(\sqrt{75}-\sqrt{27}\)?
Answer and explanation
Correct answer: \(2\sqrt{3}\)
Simplify the radicals by factoring out square factors: \(\sqrt{75}=\sqrt{25\cdot3}=5\sqrt{3}\) and \(\sqrt{27}=\sqrt{9\cdot3}=3\sqrt{3}\). Subtracting gives \(5\sqrt{3}-3\sqrt{3}=2\sqrt{3}\), so option A is correct. Option B (\(\sqrt{3}\)) is a common distractor arising from subtracting the radical parts incorrectly (treating coefficients as 1 and 0); it equals \(1\sqrt{3}\), not \(2\sqrt{3}\). Exam tip: always factor numbers under the root into square × non-square, simplify each surd, then combine like surds; if unsure, compare decimal values to check your result quickly.
Frequently asked questions
What is the correct answer to this question?
\(2\sqrt{3}\)
Why is this the correct answer?
Simplify the radicals by factoring out square factors: \(\sqrt{75}=\sqrt{25\cdot3}=5\sqrt{3}\) and \(\sqrt{27}=\sqrt{9\cdot3}=3\sqrt{3}\). Subtracting gives \(5\sqrt{3}-3\sqrt{3}=2\sqrt{3}\), so option A is correct. Option B (\(\sqrt{3}\)) is a common distractor arising from subtracting the radical parts incorrectly (treating coefficients as 1 and 0); it equals \(1\sqrt{3}\), not \(2\sqrt{3}\). Exam tip: always factor numbers under the root into square × non-square, simplify each surd, then combine like surds; if unsure, compare decimal values to check your result quickly.
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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