Finding the Third Proportional to 82,458 and 178,038

Step by Step Solution

1. Step 1: Write the proportion equation
   82,458 : 178,038 = 178,038 : x
2. Step 2: Convert to fraction form
   82,458/178,038 = 178,038/x
3. Step 3: Cross multiply
   82,458x = 178,038 × 178,038
4. Step 4: Simplify right side
   82,458x = 31,697,529,444
5. Step 5: Solve for x
   x = 31,697,529,444/82,458
6. Step 6: Final answer
   x = 384,408.18