Answer: Brandon's method is not correct
Here's why:
Let's use his method to find the square root of 36. That means we multiply 36 by 1/2 = 0.5 to get 36*0.5 = 18; however, 18 is not the square root of 36. We can see that 18*18 = 324. Instead, the square root of 36 is 6 because 6*6 = 36.
As another example, let's say we want to find the square root of 64. With Brandon's method, we would get to 64*0.5 = 32, but 32*32 = 1024. Ashley's method is correct and 8*8 = 64 shows that 8 is the square root of 64.
As a visual approach, think of a square with side lengths 8 feet each. The area would be 8*8 = 64 square feet. If you didn't know the side length, but you knew that the area was 64 square feet, then you could apply the square root operation to find the side length to be 8 feet (or you could effectively use Ashley's guess-and-check method to arrive at 8 feet). In short, the square root operation is the opposite of squaring a number. We consider these inverse operations.
Multiplying by 1/2 is the same as dividing by 2. Division is the opposite of multiplication, and division is not the inverse of squaring a number. It's just a coincidence that Brandon's method happened to work on the value 4. But as shown earlier, it doesn't work in general.