How many irrational numbers are there between 11−−√

Question

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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Answer 1

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.