Classify the following numbers as rational or irrational :
i)\(2 - \sqrt{5}\)
ii)\((3 + \sqrt{23}) - \sqrt{23}\)
iii)\( \frac{2\sqrt{7} }{ 7\sqrt{7}} \)
iv)\(\frac{1}{\sqrt{2}} \)
v)\(2\pi\)

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.