Okay, let's solve this step-by-step:
3√2 + 1 ÷ 2√5 - 3
= 3√2 + 1 / 2√5 - 3 (perform division first)
= 3*√(2) + 1 / 2*√(5) - 3 (expand square roots)
= 3*1.414 + 1 / 2*2.236 - 3 (evaluate square roots)
= 4.242 + 0.447 - 3
= 4.689
So the final simplified expression is:
4.689