Q.pruning and transplanting
i have endless summer hydrangeas. they are 8 or 9 years old. they grow a rather heavy, i don’t know whether to call it a root or a shoot but it is a growth that is growing on top of the ground. these things have a few hair type roots on the bottom and stems on top that bloom. my question is can i cut these off and transplant them to obtain additional plants?

It can be quite common to find on older Hydrangea fibrous roots on the edges of the plants.
You can try division of the roots, though it may not be a successful as propagating from cuttings.
Here are some links with more information.
https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/green-hydrangea-blooms.htm
https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-propagation.htm