Complex number magnitude value approximation

There exist a equation to approximate the complex number
x = I + j*Q  

Mag ~= Alpha * max(|I|, |Q|) + Beta * min(|I|, |Q|) , but what value of Alpha and Beta should we choose to approximate the best ?

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We actually will focus on RMS approximation error and Peak error, if we focus on RMS error only, then Beta value choose to be ¼ will be good, but the ¼ case Peak error performance are too bad. And Beta choose to be 11/32 will be the best approximation. But this case will be not easy to implement in hardware design.è Therefore we choose 3/8 as the Beta.

Which finally we will choose (1, 3/8) as the magic number for approximation.