Simplify `sqrt(52 xx 27 div 6 + 26 - 4) = ?`

Options

A. `sqrt(24)`
B. `(16)^(2)`
C. 24
D. None of these

Answer

To simplify the expression \( \sqrt{52 \times 27 \div 6 + 26 - 4} \), we will follow the order of operations (BODMAS/BIDMAS). Let's break it down step by step.

### Step 1: Simplify the multiplication and division
We start with the expression inside the square root:

\[ 52 \times 27 \div 6 \]

First, we perform the division:

\[ 27 \div 6 = \frac{27}{6} = 4.5 \]

Now, multiply this result by 52:

\[ 52 \times 4.5 = 234 \]

### Step 2: Add and subtract the remaining terms
Next, we add and subtract the other terms in the expression:

\[ 234 + 26 - 4 \]

First, add 26:

\[ 234 + 26 = 260 \]

Then, subtract 4:

\[ 260 - 4 = 256 \]

### Step 3: Take the square root
Now we take the square root of the result:

\[ \sqrt{256} \]

The square root of 256 is:

\[ 16 \]

### Final Answer
Thus, the simplified result is:

\[ \sqrt{52 \times 27 \div 6 + 26 - 4} = 16 \]

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