Concept:
In plant physiology and agronomy, several methods exist to grow plants without using natural soil. These methods differ based on what medium, if any, supports the plant roots.
Step 1: Understand the terms.
Aquaculture refers to farming aquatic animals like fish and shellfish, not to growing plants, so it does not fit here.
Soilless culture is the broad umbrella term for any plant growth method that avoids natural soil, and it covers several different techniques such as growing in sand, gravel, rockwool, or a nutrient solution alone.
Nutrient culture is used loosely at times, but it is not the precise technical term for growth restricted to a liquid mineral solution.
Step 2: Match the description given.
The question says growth happens "without soil in mineral nutrient solutions", meaning the roots are suspended directly in a liquid solution of mineral nutrients, with no solid rooting medium at all.
This exact method, where terrestrial plant roots grow immersed in an aerated nutrient solution, is called solution culture, also known as water culture, a specific type of hydroponics.
Step 3: Eliminate the other options.
Soilless culture also covers sand culture or gravel culture, where a solid but soil-free medium supports the roots, so it is too broad to be the exact answer here.
Aquaculture is unrelated to terrestrial plant nutrition.
Nutrient culture is not the standard technical name used in agronomy texts for this practice.
Final Answer:
The precise term for growing terrestrial plants without soil, with roots directly in a mineral nutrient solution, is solution culture.
\[ \boxed{\text{Solution culture}} \]