(b) State whether each of the following numbers are rational, irrational or neither. \[ \begin{array}{llll}\text { (1) } \sqrt[3]{33} & \text { (2) } \frac{\pi}{2} & \text { (3) } 4,01345 & \text { (4) } \sqrt{\frac{1}{121}} \\ \text { (5) } \sqrt{-2} & \text { (6) }-\sqrt{2} & \text { (7) } \frac{\sqrt{2}}{\sqrt{2}} & \text { (8) } \sqrt[3]{27+1}\end{array} \]

(1) \(\sqrt[3]{33}\) is irrational since it cannot be expressed as a fraction of two integers. (2) \(\frac{\pi}{2}\) is also irrational because \(\pi\) is irrational, and the division of an irrational number by a non-zero rational number remains irrational. (3) \(4,01345\) is rational because it can be expressed as a simple fraction (i.e., \(401345/100000\)). (4) \(\sqrt{\frac{1}{121}} = \frac{1}{11}\) is rational since both the numerator and denominator are integers. (5) \(\sqrt{-2}\) is neither rational nor irrational; it is considered an imaginary number. (6) \(-\sqrt{2}\) is irrational because \(\sqrt{2}\) is irrational and multiplying by \(-1\) does not change that. (7) \(\frac{\sqrt{2}}{\sqrt{2}} = 1\) is rational because it simplifies to a whole number. (8) \(\sqrt[3]{27+1} = \sqrt[3]{28}\) is irrational since 28 is not a perfect cube and cannot be expressed as a fraction of two integers.