If `18,x,x,256` are proportion, find x.

Answer

To solve the problem where \( 18, x, x, 256 \) are in proportion, we can follow these steps:

### Step 1: Set up the proportion
We know that if four numbers \( a, b, c, d \) are in proportion, then:
\[ \frac{a}{b} = \frac{c}{d} \]
In our case, we can write:
\[ \frac{18}{x} = \frac{x}{256} \]

### Step 2: Cross-multiply
Cross-multiplying gives us:
\[ 18 \cdot 256 = x \cdot x \]
This simplifies to:
\[ 18 \cdot 256 = x^2 \]

### Step 3: Calculate \( 18 \cdot 256 \)
Now, we calculate \( 18 \cdot 256 \):
\[ 18 \cdot 256 = 4608 \]
So we have:
\[ x^2 = 4608 \]

### Step 4: Solve for \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{4608} \]

### Step 5: Simplify \( \sqrt{4608} \)
To simplify \( \sqrt{4608} \), we can factor \( 4608 \):
\[ 4608 = 18 \cdot 256 = 18 \cdot (16 \cdot 16) = 18 \cdot 16^2 \]
Thus:
\[ \sqrt{4608} = \sqrt{18 \cdot 16^2} = 16 \cdot \sqrt{18} \]
Now, we can simplify \( \sqrt{18} \):
\[ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \]
So:
\[ x = 16 \cdot 3\sqrt{2} = 48\sqrt{2} \]

### Final Answer
Thus, the value of \( x \) is:
\[ x = 48\sqrt{2} \]

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