Suppose you have been given $x$ and $y$ in metres, and you'd like to know the quantity, $z=\sqrt{x^2+y^2}$. Then, as you have predicted this quatity will be in metres.
Two things have been involved:
Homogeneity of Dimension
Two quantities of different dimensions cannot be added. This is one of the axioms of numerical physics.
Example: It is clear that adding $5$ metres to $3$ seconds does not give a physically meaningful quantity that can be interpreted in real life.
Certain functions only take values in dimensionless quantities
For instance, $\sin (\sqrt{x^2+y^2})$ would not make sense even if $x$ and $y$ have same dimensions. This is a bit subtler, but this is what it is!
Coming to your question, the first quantity you tell us in dimension of $m^{1/2}$ which is against your guess!
The second quantity is dimensionally fine while numerically this is not what you want.
The third quantity is fine in all ways.
My suggestion:
First manipulate the numbers and then the units separately. This is a good practice in Numerical Physics. The other answers have done it all at one go. But, I don't prefer it that way!