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

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

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

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

v)\(2\pi\)

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.

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