Find the fourth proportional to 2, 4,and 8.

Options

A. 15
B. 14
C. 16
D. 18

Answer

To find the fourth proportional to the numbers 2, 4, and 8, we can use the concept of proportionality. The fourth proportional (let's call it D) to three numbers A, B, and C can be found using the relationship:

\[ \frac{A}{B} = \frac{C}{D} \]

Here, we have:
- A = 2
- B = 4
- C = 8
- D = ? (the fourth proportional)

### Step 1: Set up the proportion
According to the formula, we can write:

\[ \frac{2}{4} = \frac{8}{D} \]

### Step 2: Cross-multiply
Cross-multiplying gives us:

\[ 2 \cdot D = 4 \cdot 8 \]

### Step 3: Calculate the right side
Now, calculate the right side:

\[ 4 \cdot 8 = 32 \]

So, we have:

\[ 2D = 32 \]

### Step 4: Solve for D
Now, divide both sides by 2 to find D:

\[ D = \frac{32}{2} = 16 \]

### Conclusion
Thus, the fourth proportional to 2, 4, and 8 is:

\[ \boxed{16} \]