Which of the following is the simplified form of (\sqrt{80})?
Answer and explanation
Correct answer: 4\sqrt{5}
\(\sqrt{80}=\sqrt{16\times5}=\sqrt{16}\,\sqrt{5}=4\sqrt{5}\), so option A is correct. Option C (\(2\sqrt{5}\)) is only half of the correct value and option B (\(8\sqrt{5}\)) is twice as large, so both are incorrect. Option D (\(10\sqrt{2}\)) is numerically different (about 14.14) from \(4\sqrt{5}\) (about 8.94). Exam tip: always pull out the largest perfect square factor from under the root (here 16) and use \(\sqrt{a\times b}=\sqrt a\,\sqrt b\).
Frequently asked questions
What is the correct answer to this question?
4\sqrt{5}
Why is this the correct answer?
\(\sqrt{80}=\sqrt{16\times5}=\sqrt{16}\,\sqrt{5}=4\sqrt{5}\), so option A is correct. Option C (\(2\sqrt{5}\)) is only half of the correct value and option B (\(8\sqrt{5}\)) is twice as large, so both are incorrect. Option D (\(10\sqrt{2}\)) is numerically different (about 14.14) from \(4\sqrt{5}\) (about 8.94). Exam tip: always pull out the largest perfect square factor from under the root (here 16) and use \(\sqrt{a\times b}=\sqrt a\,\sqrt b\).
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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