How many integers fall between $\sqrt5$ and $\sqrt{50}$ on a number line?
The least integer greater than $\sqrt{5}$ is $\sqrt{9}=3$.  The greatest integer less than $\sqrt{50}$ is $\sqrt{49}=7$.  There are $7-3+1=\boxed{5}$ integers between 3 and 7 inclusive.
5
Level 3
Prealgebra
Problem: How many integers fall between $\sqrt5$ and $\sqrt{50}$ on a number line?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine how many integers lie between $\sqrt{5}$ and $\sqrt{50}$, we first need to calculate the approximate values of these square roots. 

Calculating $\sqrt{5}$, we know that $2^2 = 4$ and $3^2 = 9$, so $\sqrt{5}$ is between 2 and 3. A more precise approximation gives $\sqrt{5} \approx 2.236$.

Next, we calculate $\sqrt{50}$. We can express $\sqrt{50}$ as $\sqrt{25 \cdot 2} = 5\sqrt{2}$. Since $\sqrt{2} \approx 1.414$, we find that $5\sqrt{2} \approx 5 \cdot 1.414 \approx 7.07$. Thus, $\sqrt{50} \approx 7.071$.

Now we have the approximate bounds: $\sqrt{5} \approx 2.236$ and $\sqrt{50} \approx 7.071$. 

Next, we identify the integers that fall between these two values. The smallest integer greater than $\sqrt{5}$ is 3, and the largest integer less than $\sqrt{50}$ is 7. 

The integers in this range are 3, 4, 5, 6, and 7. 

Counting these integers gives us a total of 5 integers. 

Thus, the final answer is 5.<|END_OF_LATENT|> The final answer is $5$.