The Core Idea

Given an array of $n$ elements, divide it into blocks of size $B \approx \sqrt{n}$. For $n = 16$, you'd have $4$ blocks of size $4$.

Each block precomputes something useful: sum, min, max, or whatever your query needs.

A range query then combines at most $2$ partial blocks (at the ends) plus complete blocks in the middle. Why $\sqrt{n}$?

It balances two costs: the number of blocks ($n/B$) and the block size ($B$). When $B = \sqrt{n}$, both are $\sqrt{n}$, giving you $O(\sqrt{n})$ time for queries and updates. Any other block size would make one term dominate.