If \(y=\sqrt{2}+\sqrt{32}\), what is the simplified form of \(y\)?
Answer and explanation
Correct answer: \(5\sqrt{2}\)
Since \(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\), we get \(y=\sqrt{2}+4\sqrt{2}=5\sqrt{2}\). Note that \(\sqrt{a}+\sqrt{b}\) cannot be combined as \(\sqrt{a+b}\), so \(\sqrt{34}\) is incorrect. The option \(4\sqrt{2}\) would be the result only if the extra \(\sqrt{2}\) were omitted. Exam tip: always factor the radicand into perfect square factors to extract like radicals before adding or subtracting.
Frequently asked questions
What is the correct answer to this question?
\(5\sqrt{2}\)
Why is this the correct answer?
Since \(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\), we get \(y=\sqrt{2}+4\sqrt{2}=5\sqrt{2}\). Note that \(\sqrt{a}+\sqrt{b}\) cannot be combined as \(\sqrt{a+b}\), so \(\sqrt{34}\) is incorrect. The option \(4\sqrt{2}\) would be the result only if the extra \(\sqrt{2}\) were omitted. Exam tip: always factor the radicand into perfect square factors to extract like radicals before adding or subtracting.
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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