1. The problem asks which numbers are irrational among: -2.3456, \frac{\pi}{4}, \sqrt[3]{9}, 2 + \sqrt{16}. 2. Recall that an irrational number cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion. 3. Analyze each number: - -2.3456 is a decimal number with a finite number of digits, so it is rational. - \frac{\pi}{4} is \pi divided by 4. Since \pi is irrational, dividing by 4 (a rational number) keeps it irrational. - \sqrt[3]{9} is the cube root of 9. Since 9 is not a perfect cube, \sqrt[3]{9} is irrational. - 2 + \sqrt{16} equals 2 + 4 = 6, which is rational. 4. Therefore, the irrational numbers are \frac{\pi}{4} and \sqrt[3]{9}. 5. For the second question, \sqrt{24} is between \sqrt{16} = 4 and \sqrt{25} = 5, so it lies between 4 and 5 on the number line, closer to 5. Final answers: - Irrational numbers: \frac{\pi}{4} and \sqrt[3]{9} - \sqrt{24} is located between 4 and 5 on the number line, closer to 5.