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

Question

Responses

six numbers
six numbers

an infinite number
an infinite number

four numbers
four numbers

twenty-eight numbers

Answer 1

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

• \( \sqrt{11} \) is approximately \( 3.3166 \)
• \( \sqrt{17} \) is approximately \( 4.1231 \)

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

Within any interval of real numbers, there are infinitely many irrational numbers. This is because between any two real numbers (rational or irrational), you can always find another rational or irrational number.

Thus, the correct answer is:

an infinite number.