How many irrational numbers are there between 11−−√ and 17−−√ ?(1 point)

Question

Responses

four numbers
four numbers

an infinite number
an infinite number

six numbers
six numbers

twenty-eight numbers

Answer 1

To find the number of irrational numbers between \( \sqrt{11} \) and \( \sqrt{17} \), we first need to determine the approximate values of these square roots:

1. \( \sqrt{11} \approx 3.3166 \)
2. \( \sqrt{17} \approx 4.1231 \)

The interval between \( \sqrt{11} \) and \( \sqrt{17} \) is approximately \( (3.3166, 4.1231) \).

Since there are infinitely many irrational numbers in any interval of real numbers (as the real numbers are dense), there are indeed an infinite number of irrational numbers between \( \sqrt{11} \) and \( \sqrt{17} \).

Thus, the correct response is:

an infinite number.