Question

how does loosening of soil allow the roots to breathe

Answer 1

Roots doesnt breathe... The taking in of Oxygen and releasing of Carbondioxide exchange is the work of the leaves...Roots absorbs water and essential minerals for the plant.
In fact, if the soil loosens... the plant will not be able to balance itself and falls... which might probably eventually die.

Answer 2

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☞Loosening of soil allows the roots to breathe easily, because it allows them to penetrate into the spaces in between the soil particles which have air trapped in them.