Question

How many irrational numbers are there between 11−−√ and 17−−√?(1 point)%0D%0AResponses%0D%0A%0D%0Asix numbers%0D%0Asix numbers%0D%0A%0D%0Aan infinite number%0D%0Aan infinite number%0D%0A%0D%0Afour numbers%0D%0Afour numbers%0D%0A%0D%0Atwenty-eight numbers%0D%0Atwenty-eight numbers

Answer 1

To find how many irrational numbers are between \( \sqrt{11} \) and \( \sqrt{17} \), we can first approximate these square roots.

Calculating the square roots roughly:

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

Thus, we are looking for the irrational numbers between approximately 3.3166 and 4.1231.

Between any two distinct real numbers, there are infinitely many irrational numbers. Therefore, the number of irrational numbers between \( \sqrt{11} \) and \( \sqrt{17} \) is infinite.

The correct response is:

**an infinite number**.