Answer
$\dfrac{\sqrt{10}}{5}$
Work Step by Step
RECALL:
(i) For any nonnegative real number $a$, $\sqrt{a} \cdot \sqrt{a} = a$.
(ii) For any nonnegative real numbers a and b, $\sqrt{a}\cdot\sqrt{b} = \sqrt{ab}$.
Rationalize the denominator by multiplying $\sqrt{5}$ to the numerator and the denominator. Then, use the rules above to obtain
$\dfrac{\sqrt{2}}{\sqrt{5}} \cdot \dfrac{\sqrt{5}}{\sqrt{5}}
\\=\dfrac{\sqrt{10}}{5}.$
Simplify by canceling the common factor to obtain
$\require{cancel}
\dfrac{\cancel{2}\sqrt{10}}{\cancel{2}(5)}
\\=\dfrac{\sqrt{10}}{5}.$
