TITLE: Squaring both sides when units are different?
QUESTION [10 upvotes]: Given $((9) \text{inches})^{1/2} = ((0.25) \text{yards})^{1/2}$, then which of the following statements is true?

$((3) \text{inches}) = ((0.5) \text{yards})$
$((9) \text{inches}) = ((1.5) \text{yards})$
$((9) \text{inches}) = ((0.25) \text{yards})$
$((81) \text{inches}) = ((0.0625) \text{yards})$


My question is : Can I apply here as $x^{1/2}=y^{1/2}$ then square both sides $\implies x=y$. But as given units are different. So, 

Can you explain it, please?

REPLY [2 votes]: Answer 3. is correct.
If you say for linear measure
$$ 1 ft = 12 \, in, $$
then for area measure
$$ 1 ft^2 = 144 \, in^2, $$
and
$$ 1 ft^3 = 1728 \, in^3, $$
For derived units
Speed
$$ 1 ft/ \min = 12/60 = 0.2 in/\sec, $$
Rate of discharge or volume rate
$$   3600 m^3 / hour = 1 m^3/\sec, $$
and so on.