What is the domain of the function y=sqrt x?

Square root is not defined to for negative values. For negative values, the answer of square root is a complex number which is not in Real Domain.

So any such values, for which the expression is not defined are not in the Domian. So the domian of square root of x will be All real numbers greater than or equal to 0. 

This can be expressed as:

[0 , ∞)
or
x ≥ 0

For this case we have the following function:
 y = sqrt x
 We must check the values of x for which the function is defined.
 We have then:
 x> 0
 Therefore, the domain of the function is given by:
 [0, inf)
 
 [0, inf)