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Answer :
i) Irrational number (Since, 2 is a rational number and 5 is an irrational number).
Therefore, \(2 - \sqrt{5}\) is an irrational number.
ii)\((3 + \sqrt{23}) - \sqrt{23}= 3\) i.e. rational number .
iii) \(\frac{2\sqrt{7} }{7\sqrt{7}} = \frac{2}{7} \) i.e. rational number
iv) \(\frac{1}{ \sqrt{2}} \) is an irrational number because, as numerator is a rational number but denominator is an irrational number.
v) \(2\pi\) is a Irrational number , since 2 is a rational number and \(\pi\) is an irrational number. And product of rational number and irrational number is also irrational number.