What is the difference between multiplying and adding radical expressions

When adding them  you treat the radical part as if it were a variable
So we have:-

2 sqrt3 + sqrt3  = 3 sqrt3

compare:-

2x + x = 3x

When multiplying you perform a multiplcation
of the number within the radical 

Example  sqrt 2  * sqrt 3  = sqrt(2+3)  = sqrt 6

The year before the 10s so it was like when caveman were alive