Can a negative radical be expressed in terms of positive radical?

Question

I want to get rid of negative radicals, but I guess this is not possible. Assume I have:

$$-\sqrt{c}$$

Where $c$ is from $\mathbb Q^+$. Can I express this as follows, where a and b are from $\mathbb Q^+$:

$$-a + \sqrt{b}$$

Answer 1

$$-\sqrt{c}=-a + \sqrt{b}$$ $$c=a^2 -2a\sqrt{b} + b$$

This could happen, but only when at least $\sqrt{b}$ is a rational number, and thus $\sqrt{c}$ has to be a rational number as well - not an interesting case.