Suppose you had 7 square inches and wanted that converted to square centimeters. Then since 1 inch is 2.54 cm then 1 square inch is (2.54 cm)^2 = 2.54^2 cm^2 . So 7 square inches would be 7 * 2.54^2 = 45.1612 square centimeters.
Your proposal would have been for sqrt(7) * 2.54^2 = 6.7202 cm^2 . That is obviously wrong as a cm is smaller than an inch so 7 square inches cannot convert to less than 7 square centimeters.
What you can do is (sqrt(7) * 2.54)^2 which includes squaring the entire value not just the conversion factor. That will work fine (at least for positive areas ;-) ) But look again at the expression and expand it and you see that the sqrt(7) is going to get squared and multiplied by 2.54^2, so that is going to be the same as just taking the original 7 and multiplying it by the square of the conversion factor. You therefore might as well not bother taking the square root, and doing will at best be a waste of time and at worst will introduce numeric error for no benefit.
