Question

write square roots of all prime numbers and mention to which number set is a subset.

Answer 1

Prime numbers set =
        P =    { 2, 3, 5, 7 , 11, 13,  17, 19, 23 .... }
Square roots of prime numbers
         = S = { √2, √3, √5,√7, √11, √13, √17, √19, √23, .. }

√2 = 1.414....
√3 = 1.732...
so these are irrational numbers as they cannot be expressed ins p/q form.

So set of square roots of prime numbers is a subset of  irrational number set.

Irrational numbers set is a subtraction of  rational number set from real number set.