Which of the following correctly describes the nature of \(\sqrt[3]{343}\)?
Answer and explanation
Correct answer: Rational number
\(\sqrt[3]{343}=7\) since 343 is a perfect cube (\(7^3=343\)) and its cube root is an integer. Every integer is rational (e.g. \(7=7/1\)). Option B (irrational) is incorrect because irrational numbers are non‑terminating, non‑repeating decimals, unlike 7 which is a terminating integer. Option C (non‑real) is incorrect because 7 is a real number. Option D is incorrect because 7 has a terminating decimal representation (7.0), not a non‑terminating non‑repeating decimal. Exam tip: first check if the radicand is a perfect power corresponding to the root; if it is, the root is an integer (hence rational).
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What is the correct answer to this question?
Rational number
Why is this the correct answer?
\(\sqrt[3]{343}=7\) since 343 is a perfect cube (\(7^3=343\)) and its cube root is an integer. Every integer is rational (e.g. \(7=7/1\)). Option B (irrational) is incorrect because irrational numbers are non‑terminating, non‑repeating decimals, unlike 7 which is a terminating integer. Option C (non‑real) is incorrect because 7 is a real number. Option D is incorrect because 7 has a terminating decimal representation (7.0), not a non‑terminating non‑repeating decimal. Exam tip: first check if the radicand is a perfect power corresponding to the root; if it is, the root is an integer (hence rational).
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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