Damping constant and angular frequency

[bacon]

While discussing $ω^{'}$, the angular frequency of a damped harmonic oscillator, given by:
$ω^{'}=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}}}$
where k is the "springiness", m is the mass, and b is the damping constant,
my book, Halliday, Resnick and Walker, says if b is small but not zero,$b<<\sqrt{km}$ then $ω^{'}\approxω$. $ω=\frac{k}{m}$, the undamped frequency.

If I say that $\frac{k}{m}>>\frac{b^{2}}{4m^{2}}$and go through the algebra to get the relation in the book, I get $b<<\sqrt{2km}$
Is this a meaningful difference when talking about a quantity that is much, much less than another?
Thanks for any help.

 

[Redbelly98]

The two statements, $b \ll \sqrt{km} \text{ and } b \ll \sqrt{2km}$, are essentially considered to be equivalent statements.