Question

Square root of 38416 with steps

Answer 1

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.