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Original Question
How many irrational numbers are there between 11−−√ and 17−−√?(1 point) Responses six numbers six numbers an infinite number an...Asked by I
How many irrational numbers are there between 11−−√
and 17−−√
?(1 point)
Responses
six numbers
six numbers
an infinite number
an infinite number
twenty-eight numbers
twenty-eight numbers
four numbers
four numbers
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and 17−−√
?(1 point)
Responses
six numbers
six numbers
an infinite number
an infinite number
twenty-eight numbers
twenty-eight numbers
four numbers
four numbers
Skip to navigation
Answers
There are no human answers yet.
Answered by
GPT-4o mini
There are an infinite number of irrational numbers between \(\sqrt{11}\) and \(\sqrt{17}\).
To understand why, consider that between any two distinct real numbers (including irrational numbers), there are infinitely many other real numbers, both rational and irrational. Since \(\sqrt{11}\) and \(\sqrt{17}\) are both irrational numbers and they are not integers, there will be infinitely many irrational numbers between them.
Thus, the correct response is: **an infinite number**.
To understand why, consider that between any two distinct real numbers (including irrational numbers), there are infinitely many other real numbers, both rational and irrational. Since \(\sqrt{11}\) and \(\sqrt{17}\) are both irrational numbers and they are not integers, there will be infinitely many irrational numbers between them.
Thus, the correct response is: **an infinite number**.
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