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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)\(1 / \sqrt{2}\)
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) \(2\sqrt{7} / 7\sqrt{7} = 2/7\) 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.