To determine which of the given numbers are rational, we need to understand that a rational number can be expressed as a fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\).
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194.265: This is a decimal number that can be expressed as a fraction. It can be written as \(\frac{194265}{1000}\), so it is a rational number.
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√289: The square root of 289 is 17. Since 17 can be expressed as \(\frac{17}{1}\), it is a rational number.
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765.4: This is also a decimal number that can be expressed as a fraction. It can be written as \(\frac{7654}{10}\), so it is a rational number.
In conclusion, all three numbers—194.265, √289 (which is 17), and 765.4—are rational numbers.