11 answers
No, \(2 \frac{1}{2}\) (or 2.5) is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and \(2 \frac{1}{2}\) can be converted to the improper fraction \(\frac{5}{2}\), which confirms that it is rational.
Irrational numbers, on the other hand, cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions (like \(\sqrt{2}\) or \(\pi\)).
No, \(\frac{8}{3}\) is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and \(\frac{8}{3}\) is already in that form, where 8 and 3 are both integers. Since it can be represented as a fraction, it is classified as rational.
Irrational numbers cannot be expressed as such fractions and have decimal representations that are non-repeating and non-terminating. Examples of irrational numbers include numbers like \(\sqrt{2}\) and \(\pi\).
No, the square root of 1 is not an irrational number; it is a rational number. The square root of 1 is equal to 1, which can be expressed as the fraction \(\frac{1}{1}\). Since it can be represented as a fraction of two integers, it is classified as rational.
In general, any perfect square (like 1, 4, 9, etc.) has a rational square root.
No, 0 is not an irrational number; it is a rational number. A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. Since 0 can be expressed as \(\frac{0}{1}\) or \(\frac{0}{n}\) (for any non-zero integer \(n\)), it fits the definition of a rational number.
Irrational numbers, on the other hand, cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include \(\sqrt{2}\) and \(\pi\).
No, \(\frac{4}{3}\) is not an irrational number; it is a rational number. Rational numbers are defined as numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Since \(\frac{4}{3}\) is already in the form of a fraction, it is classified as a rational number.
Irrational numbers, on the other hand, cannot be expressed as a fraction of two integers and have decimal representations that are non-terminating and non-repeating. Examples of irrational numbers include \(\sqrt{2}\) and \(\pi\).
Yes, the square root of 27 is an irrational number.
The square root of 27 can be simplified as follows:
\[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3} \]
Since \(\sqrt{3}\) is an irrational number (it cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion), \(3\sqrt{3}\) is also considered irrational. Therefore, \(\sqrt{27}\) is an irrational number.
