How many irrational numbers are there between 11−−√

Question

and 17−−√
?(1 point)
Responses

four numbers
four numbers

twenty-eight numbers
twenty-eight numbers

six numbers
six numbers

an infinite number

Answer 1

There are an infinite number of irrational numbers between \(\sqrt{11}\) and \(\sqrt{17}\).

To understand why, recall that between any two distinct real numbers, there are infinitely many irrational numbers. Since \(\sqrt{11}\) and \(\sqrt{17}\) are both irrational, and since they are distinct (because \(\sqrt{11} \approx 3.3166 < \sqrt{17} \approx 4.1231\)), it follows that there are infinitely many irrational numbers between them.

Thus, the correct response is:

an infinite number.