Question

The task is to determine the values of c for which the radical expression is a real number-- expressing the answer as an inequality or "all real numbers".

a) square root of 4x
b) square root of 5-x

how exactly do i go about solving for x?

Answer 1

Well, for the first one, x > or = 0 will work

For the second one x < or = 5

Answer 2

right. how do i determine that?

Answer 3

Using mathematical intuition. You know you can't take the square root of a negative number, so if x yields a value that is negative, you don't include those values in the solution. In my solutions of both x's, I simply made sure that the value of x will either yield at least a square root of zero, because zero is the least number that you can take a square root of.