Answer:
196
Step-by-step
Step 1: the last number of 38,416 is 6. 6 is not a perfect square.
Step 2: because 6 is not a perfect square, split the number up and add each digit together:
3 + 8 + 4 + 1 + 6 = 22
2 + 2 = 4
Step 3:
the digital root of 38,416 is 4.
4 is in the list of digital roots that are always perfect squares. We can conclude that 38,416 could be a perfect square!
Step 4: find all the factors:
1 x 38,416 2 x 19,208 4 x 9,604 7 x 5,488 8 x 4,802 14 x 2,744 16 x 2,401 28 x 1,372 49 x 784 56 x 686 98 x 392 112 x 343 196 x 196
Underlined above is the factor combination that makes 38,416 a perfect square. A number can only be a perfect square if the product of two exactly the same numbers is equal to the original number.
