How can I show $2^\sqrt{2}$ on the real numbers line?
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What do you mean by "show on the real line"? – DonAntonio Dec 11 '16 at 19:46
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something like that: http://s3.img7.ir/DVhgd.jpg – Ali Ph Dec 11 '16 at 19:48
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1@AliPh Do you mean a geometric representation of $2^{\sqrt{2}}$? – gowrath Dec 11 '16 at 19:49
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not exactly but it's better than noting – Ali Ph Dec 11 '16 at 19:51
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please try to reword your question more carefully so that people are more willing to help you. – The Count Dec 11 '16 at 20:09
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I think the OP may be trying to ask how to show the number $;2^{\sqrt2};$ is constructible... – DonAntonio Dec 11 '16 at 20:44
1 Answers
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According to the calculator, $2^{\sqrt{2}} \approx 2.665144142$. It is a transcendental number. There is no geometric construction of it.
So here it is on a number line.
Robert Israel
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@Robert first you said that it is transcedental and there is no geometric construction of it and then you represent it on number line. How?? – Vidyanshu Mishra Dec 11 '16 at 19:56
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by y=2^x you can show $2^\sqrt{2}$(when x=√2 , y= $2^\sqrt{2}) but i'm looking for a better way http://s3.img7.ir/y2IFE.png – Ali Ph Dec 11 '16 at 19:56
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This number is called "Gelfond–Schneider constant" and as transcendental it is not constructable using straight edge and pair of compasses (and possibly some other construction equipment). – z100 Dec 11 '16 at 20:06
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