Is $2^{sqrt{2}}$ rational or irrational? [closed]
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Is $2^{sqrt{2}}$ rational or irrational? What is the type of this number?
irrational-numbers
edited Dec 2 at 5:35
bof
49.4k454117
asked Dec 2 at 5:24
Snehangshu Dutta
4
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closed as off-topic by Shaun, user302797, user10354138, KReiser, Toby Mak Dec 2 at 6:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shaun, user302797, user10354138, KReiser, Toby Mak
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
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down vote
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Is $2^{sqrt{2}}$ rational or irrational? What is the type of this number?
irrational-numbers
edited Dec 2 at 5:35
bof
49.4k454117
asked Dec 2 at 5:24
Snehangshu Dutta
4
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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closed as off-topic by Shaun, user302797, user10354138, KReiser, Toby Mak Dec 2 at 6:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shaun, user302797, user10354138, KReiser, Toby Mak
If this question can be reworded to fit the rules in the help center, please edit the question.
wolframalpha.com/input/?i=2%5Esqrt+2 shows that not only is it irrational, it is also transcendental.
– Mohammad Zuhair Khan
Dec 2 at 5:27
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up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Is $2^{sqrt{2}}$ rational or irrational? What is the type of this number?
irrational-numbers
edited Dec 2 at 5:35
bof
49.4k454117
asked Dec 2 at 5:24
Snehangshu Dutta
4
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Is $2^{sqrt{2}}$ rational or irrational? What is the type of this number?
irrational-numbers
irrational-numbers
edited Dec 2 at 5:35
bof
49.4k454117
asked Dec 2 at 5:24
Snehangshu Dutta
4
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Dec 2 at 5:35
bof
49.4k454117
asked Dec 2 at 5:24
Snehangshu Dutta
4
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Dec 2 at 5:35
bof
49.4k454117
edited Dec 2 at 5:35
bof
49.4k454117
edited Dec 2 at 5:35
bof
49.4k454117
49.4k454117
asked Dec 2 at 5:24
Snehangshu Dutta
4
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 2 at 5:24
Snehangshu Dutta
4
asked Dec 2 at 5:24
Snehangshu Dutta
4
4
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Snehangshu Dutta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
closed as off-topic by Shaun, user302797, user10354138, KReiser, Toby Mak Dec 2 at 6:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shaun, user302797, user10354138, KReiser, Toby Mak
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Shaun, user302797, user10354138, KReiser, Toby Mak Dec 2 at 6:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shaun, user302797, user10354138, KReiser, Toby Mak
If this question can be reworded to fit the rules in the help center, please edit the question.
wolframalpha.com/input/?i=2%5Esqrt+2 shows that not only is it irrational, it is also transcendental.
– Mohammad Zuhair Khan
Dec 2 at 5:27
add a comment |
wolframalpha.com/input/?i=2%5Esqrt+2 shows that not only is it irrational, it is also transcendental.
– Mohammad Zuhair Khan
Dec 2 at 5:27
wolframalpha.com/input/?i=2%5Esqrt+2 shows that not only is it irrational, it is also transcendental.
– Mohammad Zuhair Khan
Dec 2 at 5:27
wolframalpha.com/input/?i=2%5Esqrt+2 shows that not only is it irrational, it is also transcendental.
– Mohammad Zuhair Khan
Dec 2 at 5:27
add a comment |
1 Answer
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This number is known as the Gelfond-Schneider constant, and as pointed out in the comments, it is transcendental. You may also be interested in the Gelfond-Schneider theorem.
answered Dec 2 at 5:37
Sambo
2,1112532
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
This number is known as the Gelfond-Schneider constant, and as pointed out in the comments, it is transcendental. You may also be interested in the Gelfond-Schneider theorem.
answered Dec 2 at 5:37
Sambo
2,1112532
add a comment |
up vote
1
down vote
This number is known as the Gelfond-Schneider constant, and as pointed out in the comments, it is transcendental. You may also be interested in the Gelfond-Schneider theorem.
answered Dec 2 at 5:37
Sambo
2,1112532
add a comment |
up vote
1
down vote
up vote
1
down vote
This number is known as the Gelfond-Schneider constant, and as pointed out in the comments, it is transcendental. You may also be interested in the Gelfond-Schneider theorem.
answered Dec 2 at 5:37
Sambo
2,1112532
This number is known as the Gelfond-Schneider constant, and as pointed out in the comments, it is transcendental. You may also be interested in the Gelfond-Schneider theorem.
answered Dec 2 at 5:37
Sambo
2,1112532
edited Dec 2 at 5:51
answered Dec 2 at 5:37
Sambo
2,1112532
answered Dec 2 at 5:37
Sambo
2,1112532
answered Dec 2 at 5:37
Sambo
2,1112532
2,1112532
add a comment |
add a comment |
Q7I2xTbSY2Wg
wolframalpha.com/input/?i=2%5Esqrt+2 shows that not only is it irrational, it is also transcendental.
– Mohammad Zuhair Khan
Dec 2 at 5:27