Evaluate :
`sqrt(3^(2) xx 6^(3) xx 24)`

Answer

To evaluate the expression \( \sqrt{3^2 \times 6^3 \times 24} \), we will follow these steps:

### Step 1: Simplify the expression inside the square root
We start with the expression:
\[ \sqrt{3^2 \times 6^3 \times 24} \]

### Step 2: Calculate \(3^2\) and \(6^3\)
First, we calculate \(3^2\) and \(6^3\):
\[ 3^2 = 9 \]
\[ 6^3 = 6 \times 6 \times 6 = 216 \]

### Step 3: Substitute the values back into the expression
Now we can substitute these values back into the expression:
\[ \sqrt{9 \times 216 \times 24} \]

### Step 4: Calculate \(9 \times 216\)
Next, we calculate \(9 \times 216\):
\[ 9 \times 216 = 1944 \]

### Step 5: Now multiply by 24
Now we multiply \(1944\) by \(24\):
\[ 1944 \times 24 \]
Calculating this gives:
\[ 1944 \times 24 = 46656 \]

### Step 6: Now we take the square root
Now we take the square root of \(46656\):
\[ \sqrt{46656} \]

### Step 7: Calculate the square root
The square root of \(46656\) is:
\[ \sqrt{46656} = 216 \]

### Final Result
Thus, the value of \( \sqrt{3^2 \times 6^3 \times 24} \) is:
\[ \boxed{216} \]