Question

How many irrational numbers are there between 11−−√ and 17−−√ ?(1 point)Responsesfour numbersfour numbersan infinite numberan infinite numbertwenty-eight numberstwenty-eight numberssix numbers

Answer 1

To determine how many irrational numbers are between \(\sqrt{11}\) and \(\sqrt{17}\), we first note that the interval between these two square roots is a continuous interval of real numbers.

Both \(\sqrt{11}\) and \(\sqrt{17}\) are irrational numbers, and the set of real numbers (including both rational and irrational numbers) between any two distinct real numbers is infinite. Since irrational numbers are dense in the real numbers, there are infinitely many irrational numbers between any two distinct irrational numbers.

Therefore, the correct response is **an infinite number**.