1.Classify the following numbers as rational or irrational :

i)\(2 - \sqrt{5}\)

ii)\((3 + \sqrt{23}) - \sqrt{23}\)

iii)\(2\sqrt{7} / 7\sqrt{7}\)

iv)\(1 / \sqrt{2}\)

v)\(2\pi\)

i)\(2 - \sqrt{5}\)

ii)\((3 + \sqrt{23}) - \sqrt{23}\)

iii)\(2\sqrt{7} / 7\sqrt{7}\)

iv)\(1 / \sqrt{2}\)

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) \(2\sqrt{7} / 7\sqrt{7} = 2/7\) i.e. rational number

iv) \(1 / \sqrt{2}\) 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.