Which of the following is the simplified form of (\sqrt{125}+\sqrt{45})?
Answer and explanation
Correct answer: 8\sqrt{5}
Simplify each term: \sqrt{125}=\sqrt{25\times5}=5\sqrt{5} and \sqrt{45}=\sqrt{9\times5}=3\sqrt{5}. Adding like surds gives 5\sqrt{5}+3\sqrt{5}=8\sqrt{5}, so A is correct. Option B (\sqrt{170}) reflects the incorrect assumption \sqrt{a}+\sqrt{b}=\sqrt{a+b}. Option D (10\sqrt{5}) is a mistaken addition of coefficients. Option C (6\sqrt{10}) arises from incorrect factorization or mixing radicands. Exam tip: always factor out perfect squares from each radicand first and then combine only like surds.
Frequently asked questions
What is the correct answer to this question?
8\sqrt{5}
Why is this the correct answer?
Simplify each term: \sqrt{125}=\sqrt{25\times5}=5\sqrt{5} and \sqrt{45}=\sqrt{9\times5}=3\sqrt{5}. Adding like surds gives 5\sqrt{5}+3\sqrt{5}=8\sqrt{5}, so A is correct. Option B (\sqrt{170}) reflects the incorrect assumption \sqrt{a}+\sqrt{b}=\sqrt{a+b}. Option D (10\sqrt{5}) is a mistaken addition of coefficients. Option C (6\sqrt{10}) arises from incorrect factorization or mixing radicands. Exam tip: always factor out perfect squares from each radicand first and then combine only like surds.
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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