Actually that is probably a good sign that fungi are working in your soil. Plants need fungi to break down particles of soil and supply your plant with nutrients.
That white growth is called a mycelium and is the fungus expanding. You could have little mushrooms show up. The fascinating thing is that the strands of the fungi tap into a plants roots and supply various nutrients to the plant while feeding on sugars supplied by the plant. Both benefit from the exchange.
The largest living organism in the world today is a honey fungus measuring 2.4 miles (3.8 km) across in the Blue Mountains in Oregon.
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