Question

which subset of the real numbers contains the square root of 50

Answer 1

The first thing you should do in this case is to know that you can rewrite the expression.
 We have then:
 root (50)
 Rewriting:
 root (2 * 25)
 5 * root (2)
 Which belongs to the set of irrational numbers.
 Answer: 
 Irrational numbers.