We need to compare $\sqrt{13}$ and $\frac{15}{4}$.

1. Problem Description

We need to compare $\sqrt{13}$ and $\frac{15}{4}$.

2. Solution Steps

First, let's approximate $\sqrt{13}$. We know that $3^2 = 9$ and $4^2 = 16$. So, $\sqrt{13}$ is between 3 and

4. Since 13 is closer to 16 than to 9, $\sqrt{13}$ is closer to 4 than to

3. Using a calculator, we find that $\sqrt{13} \approx 3.60555$.

Next, we calculate the value of $\frac{15}{4}$.

$\frac{15}{4} = 3.75$

Comparing the two values, we have:

$3.60555 < 3.75$

Therefore, $\sqrt{13} < \frac{15}{4}$.

3. Final Answer

$\sqrt{13} < \frac{15}{4}$