Uniform Distribution

Find the uniform distribution U(a,b) that has the same mean and variance as X^2 (8) distribution

The answer is: a=8+4(3)^.5 and b =8-4(3)^.5

Please show work. I have no idea where to start with this one. Thanks.

I just figured this one out, but feel free to do it anyways. It would be nice to maybe see another way of doing it. Thanks.