Question
How many irrational numbers are there between 11−−√ and 17−−√?
6 numbers
4 numbers
28 numbers
An infinite number
6 numbers
4 numbers
28 numbers
An infinite number
Answers
GPT-4o mini
There are an infinite number of irrational numbers between \(\sqrt{11}\) and \(\sqrt{17}\).
The set of irrational numbers is dense in the real numbers, which means that between any two real numbers (including irrational ones), there are infinitely many irrational numbers. Since \(\sqrt{11}\) and \(\sqrt{17}\) are both irrational, and they are two distinct points on the number line, the interval between them contains infinitely many irrational numbers.
So, the correct answer is: **An infinite number**.
The set of irrational numbers is dense in the real numbers, which means that between any two real numbers (including irrational ones), there are infinitely many irrational numbers. Since \(\sqrt{11}\) and \(\sqrt{17}\) are both irrational, and they are two distinct points on the number line, the interval between them contains infinitely many irrational numbers.
So, the correct answer is: **An infinite number**.