Finding the Third Proportional to 16,384 and 35,106

Step by Step Solution

1. Step 1: Write the proportion equation
   16,384 : 35,106 = 35,106 : x
2. Step 2: Convert to fraction form
   16,384/35,106 = 35,106/x
3. Step 3: Cross multiply
   16,384x = 35,106 × 35,106
4. Step 4: Simplify right side
   16,384x = 1,232,431,236
5. Step 5: Solve for x
   x = 1,232,431,236/16,384
6. Step 6: Final answer
   x = 75,221.63