Simplify the following roots.
`sqrt(96)`

Answer

To simplify the expression \(\sqrt{96}\), we will follow these steps:

### Step 1: Factorize 96
First, we need to factorize 96 into its prime factors.

\[ 96 = 2 \times 48 \]
\[ 48 = 2 \times 24 \]
\[ 24 = 2 \times 12 \]
\[ 12 = 2 \times 6 \]
\[ 6 = 2 \times 3 \]

So, we can write:
\[ 96 = 2^5 \times 3^1 \]

### Step 2: Rewrite the square root
Now we can express \(\sqrt{96}\) using the prime factorization we found:

\[ \sqrt{96} = \sqrt{2^5 \times 3^1} \]

### Step 3: Separate the pairs
We can separate the factors into pairs. Since \(\sqrt{a^2} = a\), we can take out pairs of 2's from under the square root.

\[ \sqrt{2^5} = \sqrt{(2^2)^2 \times 2^1} = \sqrt{(4)^2 \times 2} = 4\sqrt{2} \]

### Step 4: Combine with the other factor
Now, we can combine this with the \(\sqrt{3}\):

\[ \sqrt{96} = \sqrt{2^5 \times 3^1} = 4\sqrt{2 \times 3} = 4\sqrt{6} \]

### Final Answer
Thus, the simplified form of \(\sqrt{96}\) is:

\[ \sqrt{96} = 4\sqrt{6} \]

---