How many irrational numbers are there between the square root of11 and the square root of17? (1 point)

Answer 1

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

Calculating:

• \(\sqrt{11} \approx 3.3166\)
• \(\sqrt{17} \approx 4.1231\)

Now we know that the interval between \(\sqrt{11}\) and \(\sqrt{17}\) is approximately \([3.3166, 4.1231]\).

Since the set of real numbers is uncountable and includes both rational and irrational numbers, we can state that between any two distinct real numbers (including irrational numbers), there are infinitely many irrational numbers.

Thus, we conclude that there are infinitely many irrational numbers between \(\sqrt{11}\) and \(\sqrt{17}\).