how to write this in excel

With r in cell A1, and a in cell A2 it will be like this
=1/(2*SQRT(4*A1^2-A2^2))

Yhave two answers because your expression is ambiguous:

(1/2) * sqrt(4r^2-a^2)     or    1 / (2 * sqrt(4r^2-a^2))

@d-glitch

+1

No, it is not ambiguos. Math rules tell clearly you have to assume   1/2 * sqrt(4*r^2-a^2).

You are assuming the questioner knows the rules as well as you do.
Much better to clarify first, especially when dealing with typewriter equations.

@d-glitch

+1 again. :)

:)
Yes, it is a little bit tricky.
If you are using normal rules, then multiplication and division have the same precedence so you should start solving the equation from left to right - like (1/2)* sqrt(4*r^2-a^2)=0,5*sqrt(4*r^2-a^2)...
That is in case that poster just forgot to write multiplication sign.
In this case my comment is correct one.

But if poster did not wrote the multiplication sigh by purpose and he is using the rule that some use that implied mutiplication has precedence before division, then the formula should look like 1/(2 * sqrt(4*r^2-a^2)).
In this case Ejigl is right...

Unless I have no strong reason not to, I need to rely on what the asker tells. However, it would be much better to see
        ½√(4r²-a²)
and/or the context.

1/2 x  is different from  1/2x. The latter seems to be "ambiguous", but isn't. If you write the latter down with explicit operators, it is still (1/2)*x. Every other intended meaning is wrong.
I understand you are trying to cover wrong typing, but you should first take the posters word literally. In particular as the formula looks much more familar if interpreted strictly.

Interesting link (second part + comments):
http://blogs.ptc.com/2011/11/10/math-basics-order-of-operations-precedence-and-tricky-brainteasers/

That is why I differ between    1/2x, 1/2 x, 1/ 2x. I still say the result is the same, but the intended meaning might differ ;-).

I've requested that this question be closed as follows:

Accepted answer: 500 points for hgholt's comment #a41033574

for the following reason:

This question has been classified as abandoned and is closed as part of the Cleanup Program. See the recommendation for more details.

As discussed, there is either a single solution, then it is http:#a41033576, or the request is ambiguous, and there are two possible solutions (the first two comments).

I agree with Qlemo in the first comment.
The request is not ambiguous.

I read the question wrong, and made a mistake in the solution.
davorin has the correct solution.
Math rules clearly is that no sign means multiplication.