Math paradox?

Question

(x+5)^(1/2) + (x+10)^(1/2) >2
After solving it i get x > -79/16 however if you put -5 in the equation it works. After thinking for a bit i thought of the part where i get
1/4 < (x+5)^(1/2) and when you know that a radical has to be greater than 0, so I just switched the 1/4 with a 0 and i get x>-5 but that doesnt really seem right to me. I put the equation in the calculator and it got x >-5

Answer 1

x>= -5 is right. The equation isn't defined for x < -5. When x = -5, the first radical is 0 and the second is √5 which is 2.24 > 2. y = √x is the top half of a sideways parabola for which y increases when x increases.