Evaluate :
`sqrt((0.5)^(3) xx 6 xx 3^(5))`

Answer

To evaluate the expression \( \sqrt{(0.5)^3 \times 6 \times 3^5} \), we can follow these steps:

### Step 1: Rewrite the expression
First, we can rewrite \( 0.5 \) as a fraction:
\[ 0.5 = \frac{1}{2} \]
Thus, we can rewrite \( (0.5)^3 \) as:
\[ (0.5)^3 = \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8} \]
Now, substituting this back into the expression gives us:
\[ \sqrt{\frac{1}{8} \times 6 \times 3^5} \]

### Step 2: Simplify the expression inside the square root
Next, we can simplify the expression inside the square root:
\[ \frac{1}{8} \times 6 = \frac{6}{8} = \frac{3}{4} \]
So now we have:
\[ \sqrt{\frac{3}{4} \times 3^5} \]

### Step 3: Combine the terms
Now, we can combine \( \frac{3}{4} \) and \( 3^5 \):
\[ \frac{3}{4} \times 3^5 = \frac{3^1 \times 3^5}{4} = \frac{3^{1+5}}{4} = \frac{3^6}{4} \]
Thus, our expression now is:
\[ \sqrt{\frac{3^6}{4}} \]

### Step 4: Apply the square root
We can separate the square root:
\[ \sqrt{\frac{3^6}{4}} = \frac{\sqrt{3^6}}{\sqrt{4}} = \frac{3^{6/2}}{2} = \frac{3^3}{2} \]
Calculating \( 3^3 \):
\[ 3^3 = 27 \]
So we have:
\[ \frac{27}{2} \]

### Step 5: Final answer
Thus, the final answer is:
\[ \frac{27}{2} = 13.5 \]