The increase in length of stems and roots in plants is due to

The increase in the length of stems and roots in plants is primarily due to the activity of apical meristems. These meristems are located at the growing tips of shoots and roots. The process, known as primary growth, involves rapid cell division in the apical meristems followed by cell elongation, which allows roots to penetrate deeper into the soil and shoots to reach for sunlight. In contrast, lateral meristems are responsible for secondary growth, which increases the girth or thickness of the plant. Intercalary meristems, found mainly in monocots like grasses, contribute to rapid stem elongation by adding growth between mature tissues, but the fundamental lengthening of the main plant axis from the tips is the function of the apical meristem.

Sources

1. [1] https://www.ncbi.nlm.nih.gov/books/NBK10030/
2. [2] https://en.wikipedia.org/wiki/Primary_growth