To relate the square root function \( k(x) = \sqrt{5}x \) to the associated quadratic function, we need to find the function that represents the square of the original function.
If \( k(x) = \sqrt{5}x \), then squaring both sides gives:
\[ k(x)^2 = (\sqrt{5}x)^2 = 5x^2 \]
Therefore, the corresponding quadratic function \( m(x) \) is:
\[ m(x) = 5x^2 \]
Based on your options, the correct identification of the quadratic function related to the square root function \( k(x) = \sqrt{5}x \) is:
m(x) = 5x².