What type of number is \(\sqrt[3]{27}\)?
Answer and explanation
Correct answer: Rational number
\(\sqrt[3]{27}=3\) since \(3^3=27\). The result is an integer, and every integer is rational (can be written as a fraction, e.g. \(3=3/1\)). Option B is incorrect because irrational numbers cannot be expressed as a ratio of integers and have non-repeating, non-terminating decimals — that does not apply here. Option C is incorrect because the value is a real integer, not a non-real complex number. Option D is incorrect because the number is not a non-terminating non-repeating decimal but a terminating integer. Exam tip: first check if the radicand is a perfect power; the root of a perfect cube is an integer and hence rational.
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What is the correct answer to this question?
Rational number
Why is this the correct answer?
\(\sqrt[3]{27}=3\) since \(3^3=27\). The result is an integer, and every integer is rational (can be written as a fraction, e.g. \(3=3/1\)). Option B is incorrect because irrational numbers cannot be expressed as a ratio of integers and have non-repeating, non-terminating decimals — that does not apply here. Option C is incorrect because the value is a real integer, not a non-real complex number. Option D is incorrect because the number is not a non-terminating non-repeating decimal but a terminating integer. Exam tip: first check if the radicand is a perfect power; the root of a perfect cube is an integer and 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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