Finding the Third Proportional to 825,588 and 1,686,164

Step by Step Solution

1. Step 1: Write the proportion equation
   825,588 : 1,686,164 = 1,686,164 : x
2. Step 2: Convert to fraction form
   825,588/1,686,164 = 1,686,164/x
3. Step 3: Cross multiply
   825,588x = 1,686,164 × 1,686,164
4. Step 4: Simplify right side
   825,588x = 2,843,149,034,896
5. Step 5: Solve for x
   x = 2,843,149,034,896/825,588
6. Step 6: Final answer
   x = 3,443,786.77