Which of the following is the simplified form of \\(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\\)?
Answer and explanation
Correct answer: \\(7\sqrt{2}\\)
Like surds (same radicand) combine by adding their coefficients. The coefficients here are 5, 3 and −1, so 5+3−1 = 7, giving \\(7\sqrt{2}\\). Option B (\\(9\sqrt{2}\\)) would result from mistakenly treating −1 as +1. Option C (\\(7\sqrt{3}\\)) is wrong because the radicand changed to 3 — you cannot change the radicand when combining like surds. Option D (\\(\sqrt{14}\\)) reflects an incorrect multiplication of roots instead of combining coefficients. Exam tip: always check the radicands first — only combine terms with identical radicands by adding/subtracting their coefficients.
Frequently asked questions
What is the correct answer to this question?
\\(7\sqrt{2}\\)
Why is this the correct answer?
Like surds (same radicand) combine by adding their coefficients. The coefficients here are 5, 3 and −1, so 5+3−1 = 7, giving \\(7\sqrt{2}\\). Option B (\\(9\sqrt{2}\\)) would result from mistakenly treating −1 as +1. Option C (\\(7\sqrt{3}\\)) is wrong because the radicand changed to 3 — you cannot change the radicand when combining like surds. Option D (\\(\sqrt{14}\\)) reflects an incorrect multiplication of roots instead of combining coefficients. Exam tip: always check the radicands first — only combine terms with identical radicands by adding/subtracting their coefficients.
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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