Try to solve root in inequality got wrong result I am very confused. So I have to solve this inequality. The result is $13/24$.
But if I try to solve it myself, I get $17/24$. Because:
$$\sqrt{\left(\frac{-5}{24}\right)^2 + \frac{1}{4}} = \frac{5}{24} + \frac{1}{2} = \frac{5}{24} + \frac{12}{24} = \frac{17}{24}.$$
The right solution should be $13/24$.
Where is my failure?

$\sqrt{(-5/24)^2+1/4} = \sqrt{25/24^2+1/4} = \sqrt{(25+6\cdot 24)/24^2} = \sqrt{169}/\sqrt{24^2} = 13/24$
