Calculating Redshift to Using Hubble Constant and Distance

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To calculate the redshift of a galaxy cluster at a distance of 520 Mpc using the Hubble constant (H0 = 72 km s−1 Mpc−1), one must first determine the speed at which the cluster is receding. This speed can be calculated by multiplying the distance by the Hubble constant, yielding a value in km/s. For redshifts that are much less than 1, classical redshift calculations can be applied using the formula z = v/c, where v is the calculated speed and c is the speed of light. However, for redshifts approaching or exceeding 1, relativistic effects and the expansion of the universe must be considered. Accurate calculations depend on these factors to ensure correct interpretations of cosmic distances and velocities.
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A redshift survey has identified a galaxy cluster for which it infers a di stance of 520 Mpc. At what redshift is this cluster observed to be? You may use H0 = 72 km s−1 Mpc−1

Now call me old fashioned but don't i need some kind of relativistic speed to calculate the redshift, i mean i have a distance of 520Mpc (=16.12x10^21m) and the Hubble constant...but I am sure i need a value for how fast its traveling away from me...

Thanks

EDIT i think i just realized that i times its distance by Ho to get its speed as its Kms-1 Mpc-1
 
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Your edit is correct.
 
Then as long as this speed is much less than 'c' you can just use classical redshift.
When you get redshifts approaching (or larger than) 1 you need to take into account the expansion of the universe.
 
yeah the Lorentz factor was 1.00... so i just used z=v/c
 

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