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

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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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