Roots growing out the tops of my plants

My ludwigua does send out roots out the stalks. I don't keep them anymore now because of it
 
When I trim off all the root in my high light 29 gallon tank, the roots grow back within 2 days..

In my 10 gallon shrimp tank with no ferts and a 15 watt bulb, these plants stay growing and do not put off any side roots. These plants have been planted in my 10 gallon tank for about 2 months
 
I have the same plant, though no idea what they call. In fact, I love the look of it, including those roots, really. I always thought this is what it suppose to look like.
 
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