We are given that $\sqrt{5} = 2.236$, and we need to evaluate the expression $\frac{3}{2\sqrt{5}}$. Then, we need to simplify the expression $\frac{4!4!}{2!2!2!}$.

1. Problem Description

We are given that $\sqrt{5} = 2.236$, and we need to evaluate the expression $\frac{3}{2\sqrt{5}}$. Then, we need to simplify the expression $\frac{4!4!}{2!2!2!}$.

2. Solution Steps

First, we evaluate the expression $\frac{3}{2\sqrt{5}}$ using the approximation $\sqrt{5} = 2.236$.

$\frac{3}{2\sqrt{5}} = \frac{3}{2(2.236)} = \frac{3}{4.472} \approx 0.6708$

Next, we simplify $\frac{4!4!}{2!2!2!}$

Recall that $n! = n(n-1)(n-2)...(2)(1)$. Thus $4! = 4 \times 3 \times 2 \times 1 = 24$ and $2! = 2 \times 1 = 2$.

$\frac{4!4!}{2!2!2!} = \frac{24 \times 24}{2 \times 2 \times 2} = \frac{576}{8} = 72$.

Now, we examine the answer choices.

(a) $2! = 2$.

(b) $4! = 24$.

(c) $3 \times 4! = 3 \times 24 = 72$.

(d) $4 \times 4! = 4 \times 24 = 96$.

3. Final Answer

For the first problem, the answer is (b) $0.6708$.

For the second problem, the answer is (c) $3 \times 4!$.