Question

prove that root 2 + root 2 + root 2 + root 2 dotdotdot is a rational number

Answer 1

But,
$\sqrt{2} \: + \sqrt{2} + \sqrt{2}.....n \: \: \: times \\ = n \sqrt{2} .$
Any integer ×
$\sqrt{2}$
= Irrational number only.
So, I don't think it is irrational number.



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