Root hairs also form at the tips of regular roots as they grow through the soil. Of course, most cells are so tiny that they're practically invisible. The big roots you're seeing help anchor the plant in the ground, and they do transport water, but nearly all the plant's water is absorbed not by them, but by the root hairs. In typical soil, water is available to plants mostly as a thin film surrounding every microscopic soil particle. The branching and rebranching is what defines fibrous roots.
Fibrous roots are probably the most common root type.
The ones shown in the picture are from a weed in my garden, the Three-seeded Mercury, Acalypha rhomboidea . If you have dug up dandelions in your backyard, you've seen their tap roots. In gardens, carrots are even better tap-root examples. Oak, hickory, and conifer trees also produce tap roots, at least when young. In the case of carrots, turnips, beets, radishes, and parsnips, the storage root is also a tap root.