How many irrational numbers are there between square root of 11 and square root of 17

Answer 1

We know that $\sqrt{11}$ is less than $\sqrt{x}$, which is less than $\sqrt{17}$, where $11 < x < 17$.

Since we want to count the irrational numbers, we can disregard the rational numbers between $\sqrt{11}$ and $\sqrt{17}$.

The rational numbers between $\sqrt{11}$ and $\sqrt{17}$ are $\sqrt{12}$, $\sqrt{13}$, $\sqrt{14}$, $\sqrt{15}$, and $\sqrt{16}$.

We have to count the irrational numbers between $\sqrt{11}$ and $\sqrt{12}$, between $\sqrt{13}$ and $\sqrt{14}$, and between $\sqrt{15}$ and $\sqrt{17}$.

These are three intervals, and the number of irrational numbers in each interval is infinite.

Therefore, the total number of irrational numbers between $\sqrt{11}$ and $\sqrt{17}$ is infinite.