The Moon And The Earth, Acceleration ( Question Answered, Just need check )

[RajdeepSingh7]

The Moon And The Earth, Acceleration ( Question Answered, Just need check ) :D

The question we were given was.:

Given the facts that (i) the acceleration due to gravity at the surface of the Earth is 9.80 m/s2, (ii)
the Moon orbits the Earth every 27.32 days, and (iii) the radius of the Earth is 6.38 × 106 m,
estimate the distance, R, between the centre of the Earth and the centre of the Moon. (Hint:
write down the relevant equations and rearrange them to give expressions for R. You will find
that many of the variables cancel out).

I have attempted it and this is my answer:
2pi*R=T*v
R=2pi/(T*v)
a=v^2/R v=sqrt(aR)
R*sqrt(R)=2pi/(T*sqrt(a)) (a=acceleration(9.8m/s2), v=velocity, T=period time(27.32 days))

Is this the correct method, could anyone please tell me and clarify?
And also, how do I get rid of the sqrt(R), is there anyway to give the expression just in terms of R?

Any Help and Contribution will be greatly appreciated.
:D

 

[kuruman]

I have attempted it and this is my answer:
2pi*R=T*v
R=2pi/(T*v)

Your approach is correct however the second equation does not follow from the first. Try again.