`3sqrt(512)+2(2)/(5)div x=sqrt(25xx16)`

Options

A. 1
B. 1.4
C. 1.2
D. 0.6

Explanation

To solve the equation \( 3\sqrt{512} + \frac{2 \cdot 2}{5} \div x = \sqrt{25 \times 16} \), we will follow these steps:

### Step 1: Calculate \( \sqrt{512} \)
First, we need to simplify \( \sqrt{512} \).

\[ \sqrt{512} = \sqrt{8 \times 64} = \sqrt{8} \times \sqrt{64} = 4\sqrt{8} \]

Since \( 8 = 4 \times 2 \), we can further simplify:

\[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \]

Thus,

\[ \sqrt{512} = 4 \times 2\sqrt{2} = 8\sqrt{2} \]

Now, we have:

\[ 3\sqrt{512} = 3 \times 8\sqrt{2} = 24\sqrt{2} \]

### Step 2: Simplify \( \frac{2 \cdot 2}{5} \)
Next, we simplify \( \frac{2 \cdot 2}{5} \):

\[ \frac{2 \cdot 2}{5} = \frac{4}{5} \]

### Step 3: Substitute values into the equation
Now we substitute these values back into the equation:

\[ 24\sqrt{2} + \frac{4}{5} \div x = \sqrt{25 \times 16} \]

### Step 4: Calculate \( \sqrt{25 \times 16} \)
Next, we calculate \( \sqrt{25 \times 16} \):

\[ \sqrt{25 \times 16} = \sqrt{400} = 20 \]

### Step 5: Rewrite the equation
Now we rewrite the equation:

\[ 24\sqrt{2} + \frac{4}{5} \div x = 20 \]

### Step 6: Isolate \( \frac{4}{5} \div x \)
To isolate \( \frac{4}{5} \div x \), we subtract \( 24\sqrt{2} \) from both sides:

\[ \frac{4}{5} \div x = 20 - 24\sqrt{2} \]

### Step 7: Solve for \( x \)
Now, we can express \( \frac{4}{5} \div x \) as \( \frac{4}{5x} \):

\[ \frac{4}{5x} = 20 - 24\sqrt{2} \]

Now, we can cross-multiply to solve for \( x \):

\[ 4 = (20 - 24\sqrt{2}) \cdot 5x \]

### Step 8: Rearranging to find \( x \)
Rearranging gives:

\[ x = \frac{4}{5(20 - 24\sqrt{2})} \]

### Step 9: Simplify the expression for \( x \)
Now we can simplify this expression further if needed or calculate the numerical value.

### Final Result
Thus, the value of \( x \) is:

\[ x = \frac{4}{5(20 - 24\sqrt{2})} \]