Question

1. (adj.) very new and different; encouraging complete change (e.g., political); 2. (n.) a revolutionary, someone making huge changes; (math) an expression that uses a root (e.g., a square root)

Explanation:

The description in 1. as an adjective means innovative and promoting radical change. In 2., as a noun, it refers to a person instigating major changes. In a mathematical context, it refers to an expression with a root like a square - root. The word is "radical".

Answer:

radical