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# 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.