How many irrational numbers are there between 11−−√ and 17−−√?
First, we need to find the ceiling of $\sqrt{11}$ and the floor of $\sqrt{17}$, since the irrational numbers between $\sqrt{11}$ and $\sqrt{17}$ will correspond to the irrational numbers between $\sqrt{11}$ and $\lceil\sqrt{11}\rceil$, and between $\lfloor\sqrt{17}\rfloor$ and $\sqrt{17}$. Note that $\sqrt{11}$ is approximately $3.317$, while $\sqrt{17}$ is approximately $4.123$. Thus, the irrational numbers between $\sqrt{11}$ and $\sqrt{17}$ will correspond to the irrational numbers between $3$ and $4$. Since there are no integers between $3$ and $4$, there are $\boxed{0}$ irrational numbers between $\sqrt{11}$ and $\sqrt{17}$. (There are still infinitely many, but none of them are rational.)
To find the number of irrational numbers between √11 and √17, we need to count the irrational numbers within that range.
First, let's find the decimal approximations for √11 and √17:
√11 ≈ 3.3166
√17 ≈ 4.1231
Next, let's find the whole numbers between these decimal approximations. The whole numbers between 3.3166 and 4.1231 are 4.
Now, let's consider the irrational numbers between √11 and √17. Since both numbers are square roots, any number between them will also be a square root.
The square roots of the integers from 5 to 16 are irrational numbers between √11 and √17. So, there are a total of 12 (16-5+1) irrational numbers between √11 and √17.
Therefore, there are 12 irrational numbers between √11 and √17.