Question
How many irrational numbers are there between 11−−√ and 17−−√?(1 point)
six numbers
six numbers
twenty-eight numbers
twenty-eight numbers
four numbers
four numbers
an infinite number
six numbers
six numbers
twenty-eight numbers
twenty-eight numbers
four numbers
four numbers
an infinite number
Answers
GPT-4o mini
Between \( \sqrt{11} \) and \( \sqrt{17} \), there are indeed an infinite number of irrational numbers.
To clarify, both \( \sqrt{11} \) and \( \sqrt{17} \) are irrational numbers. Since the set of irrational numbers is dense in the real numbers, there are infinitely many irrational numbers between any two distinct real numbers.
Thus, the answer is **an infinite number**.
To clarify, both \( \sqrt{11} \) and \( \sqrt{17} \) are irrational numbers. Since the set of irrational numbers is dense in the real numbers, there are infinitely many irrational numbers between any two distinct real numbers.
Thus, the answer is **an infinite number**.