The problem asks us to find the greatest value among the following numbers: $8.7$, $\sqrt{61}$, $\frac{37}{4}$, and $3\pi$.

1. Problem Description

The problem asks us to find the greatest value among the following numbers: $8.7$, $\sqrt{61}$, $\frac{37}{4}$, and $3\pi$.

2. Solution Steps

First, let's approximate the value of each number.

* $8.7$ is already in decimal form.

* $\sqrt{61}$ is between $\sqrt{49}=7$ and $\sqrt{64}=8$. Since 61 is closer to 64, $\sqrt{61}$ is a little less than

8. We can approximate it as 7.

8. * $\frac{37}{4}$ can be written as a mixed number: $\frac{37}{4} = 9 \frac{1}{4} = 9.25$.

* $3\pi$. We know that $\pi \approx 3.14159$. Therefore, $3\pi \approx 3 \times 3.14159 = 9.42477$.

Comparing the values, we have:

$8.7$

$\sqrt{61} \approx 7.8$

$\frac{37}{4} = 9.25$

$3\pi \approx 9.42477$

Comparing the numbers, we have $7.8 < 8.7 < 9.25 < 9.42477$. Thus, $3\pi$ has the greatest value.

3. Final Answer

$3\pi$