The distance between points $ A $ and $ B $ is :
$$ d(A, B) = 0.8869 $$To find distance between points $ A(x_1,y_1)$ and $ B(x_2,y_2)$, we use formula:
$$ \color{blue}{ d(A,B) = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} } $$In this example we have:
$$ \begin{aligned} & A \left(\sqrt{ 2 },~-\dfrac{ 1 }{ 3 }\right) \implies x_1 = \sqrt{ 2 } ~~\text{and}~~ y_1 = -\frac{ 1 }{ 3 } \\[1 em] & B \left(\sqrt{ 5 },~0\right) \implies x_2 = \sqrt{ 5 } ~~\text{and}~~ y_2 = 0 \end{aligned} $$Substituting $ x_1 $, $ x_2 $, $ y_1 $ and $ y_2 $ into the formula above yields:
$$ \begin{aligned} d(A,B) & = \sqrt{\left( \sqrt{ 5 } - \sqrt{ 2 } \right)^2 + \left( 0 - \left( -\frac{ 1 }{ 3 }\right) \right)^2} \\[1 em] d(A,B) & = \sqrt{ 0.8219^2 + \left(\frac{ 1 }{ 3 }\right)^2 } \\[1 em] d(A,B) & = \sqrt{ 0.6754 + \frac{ 1 }{ 9 } } \\[1 em] d(A,B) & = \sqrt{ 0.7866 } \\[1 em] d(A,B) & = 0.8869 \end{aligned} $$