`(5(8^(1//3) + 27^(1//3) ))^(1//2) =`

Answer

To solve the expression \((5(8^{1/3} + 27^{1/3}))^{1/2}\), we will follow these steps:

### Step 1: Simplify the cube roots
First, we need to simplify \(8^{1/3}\) and \(27^{1/3}\).
- \(8\) can be expressed as \(2^3\), so:
\[ 8^{1/3} = (2^3)^{1/3} = 2^{3 \cdot (1/3)} = 2^1 = 2 \]
- \(27\) can be expressed as \(3^3\), so:
\[ 27^{1/3} = (3^3)^{1/3} = 3^{3 \cdot (1/3)} = 3^1 = 3 \]

### Step 2: Substitute back into the expression
Now, substitute these values back into the expression:
\[ (5(8^{1/3} + 27^{1/3}))^{1/2} = (5(2 + 3))^{1/2} \]

### Step 3: Add the values inside the parentheses
Now, we add \(2\) and \(3\):
\[ 2 + 3 = 5 \]
Thus, the expression becomes:
\[ (5 \cdot 5)^{1/2} \]

### Step 4: Multiply the values
Now, multiply \(5\) by \(5\):
\[ 5 \cdot 5 = 25 \]
So, we have:
\[ (25)^{1/2} \]

### Step 5: Take the square root
Finally, we take the square root of \(25\):
\[ (25)^{1/2} = 5 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{5} \]