Find the fourth proportional to 72, 168, and 150.

Answer

To find the fourth proportional to the numbers 72, 168, and 150, we can set up the relationship using the concept of proportionality.

### Step-by-Step Solution:

1. **Set up the proportion**:
We need to express the relationship as:
\[ \frac{72}{168} = \frac{150}{x} \]
Here, \(x\) is the fourth proportional we want to find.

2. **Cross-multiply**:
Cross-multiplying gives us:
\[ 72 \cdot x = 150 \cdot 168 \]

3. **Calculate \(150 \cdot 168\)**:
Now, we need to calculate \(150 \cdot 168\):
\[ 150 \cdot 168 = 25200 \]

4. **Substitute back into the equation**:
Now, we substitute this value back into the equation:
\[ 72x = 25200 \]

5. **Solve for \(x\)**:
To find \(x\), divide both sides by 72:
\[ x = \frac{25200}{72} \]

6. **Perform the division**:
Now, we calculate \(25200 \div 72\):
\[ 25200 \div 72 = 350 \]

7. **Conclusion**:
Therefore, the fourth proportional to 72, 168, and 150 is:
\[ x = 350 \]

### Final Answer:
The fourth proportional to 72, 168, and 150 is **350**.