Which of the following is the simplified form of \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?
Answer and explanation
Correct answer: 0
Simplify each radical: \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+\sqrt{20}-\sqrt{45}=\sqrt{5}+2\sqrt{5}-3\sqrt{5}=(1+2-3)\sqrt{5}=0\). The closest distractor \(-\sqrt{5}\) would arise only from an arithmetic/sign error when combining coefficients; correct combination gives zero. Exam tip: factor out the common \(\sqrt{5}\) first to add coefficients quickly.
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What is the correct answer to this question?
0
Why is this the correct answer?
Simplify each radical: \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+\sqrt{20}-\sqrt{45}=\sqrt{5}+2\sqrt{5}-3\sqrt{5}=(1+2-3)\sqrt{5}=0\). The closest distractor \(-\sqrt{5}\) would arise only from an arithmetic/sign error when combining coefficients; correct combination gives zero. Exam tip: factor out the common \(\sqrt{5}\) first to add coefficients 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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