How many irrational numbers are there between 11−−√ and 17−−√?(1 point) Responses an infinite number an infinite number six numbers six numbers four numbers four numbers twenty-eight numbers

Answer 1

To determine how many irrational numbers exist between \(\sqrt{11}\) and \(\sqrt{17}\), we first find the approximate values of these square roots.

1. \(\sqrt{11} \approx 3.316\)
2. \(\sqrt{17} \approx 4.123\)

Now, we consider the interval \( (\sqrt{11}, \sqrt{17}) \) which is approximately \( (3.316, 4.123) \).

There are infinitely many rational and irrational numbers within any interval between two numbers. Since the set of irrational numbers is dense within the real numbers, there exists an infinite number of irrational numbers in any interval, no matter how small.

Thus, the answer is:

an infinite number.