First, let's simplify the terms inside the parentheses:

√8 = √(42) = √4 √2 = 2√2
3√5 stays the same

Now, apply the distributive property:

(3√5 - 2√2) * (2√2 + 3√5) + √48

Now, multiply each term by each term in the other parentheses:

= 3√5 2√2 + 3√5 3√5 - 2√2 2√2 - 2√2 3√5 + √48

= 6√10 + 9*5 - 4 - 6√10 + √48

= 6√10 + 45 - 4 - 6√10 + 4√3

Now, combine like terms:

= 0 + 41 + 4√3

= 41 + 4√3

Therefore, (3√5 - √8) * (√8 + 3√5) + √48 simplifies to 41 + 4√3.