Remark
10*sqrt(5) is irrational because sqrt(5) is irrational. All you have done is move the decimal place from 1 place to the right. sqrt(5) = 2.2361 approximately
10 sqrt(5) = 22.361 approximately. The dominate feature of multiplication is always the irrational number. If one of the numbers is irrational when you multiply two numbers together, then the answer will be irrational.
