Equation: 1/4 - 3/16 = x.

(1/4)^2 - 3/16 = x.

1/16 - 3/16 = x.

*x = -2/16*?

OR,

1/4 - 3/16 = x.

4/16 - 3/16 = x.

*x = 1/16*?

What I did was try to establish a common denominator (turning 4 into 16), so in the first "method", I square rooted the whole thing to get a denominator of 16, because 4^2 = 16. However, 1 has a square root of 1, so theoretically, is it just wrong to square root any fraction with 1 as a numerator? Because then, you'd have fractions like 1/2 = 1/4 = 1/8 = 1/16, which doesn't sound very mathematically correct.

I understand the second part where x = 1/16 is likely the correct answer, but I can't figure out where the first part went wrong. If this sort of question has been answered already, I would appreciate a link to the post as this forum is rather big.

Thanks!