Short Answer 
The process of simplifying radical expressions includes identifying the radicand, expanding the expressions to include the radicand in a manageable format, and then simplifying by factoring out perfect squares. For example, ‚ao(3xy * 9x¬≤y¬≤) can be simplified to 3xy‚ao(3xy).
Step 1: Identify the Radicand
Start by determining the original radical expressions and their respective radicands. Look for terms that can be rewritten into the format where the radicand is a product of 3xy and a perfect square. This is essential as it sets the stage for simplification.
Step 2: Expand the Radical Expressions
Rewrite the radical expressions by expanding them to include the radicand 3xy. For instance, for ‚ao27x¬≥y¬≥, expand it as ‚ao(3xy * 9x¬≤y¬≤). This helps in segregating the perfect square part from the other components, making it easier to simplify.
Step 3: Simplify the Expressions
Once you have the expressions expanded, proceed to simplify them. Factor out the perfect square from the radical. For example, ‚ao(3xy * 9x¬≤y¬≤) simplifies to 3xy‚ao(3xy). Continue this process until all radicals are simplified into the desired format.