Limit of $lim_{xto0^+}frac{sin x}{sin sqrt{x}}$

How do I calculate this?

$$\lim_{x\to0^+}\frac{\sin x}{\sin \sqrt{x}}$$
If I tried using l'Hopital's rule, it would become
$$\lim_{x\to0^+}\frac{\cos x}{\frac{1}{2\sqrt{x}}\cos \sqrt{x}}$$
which looks the same. I can't seem to find a way to proceed from here. Maybe it has something to do with $$\frac{\sin x}{x} \to 1$$

but I'm not sure what to do with it. Any advice?

Oh and I don't understand series expansions like Taylor's series.

Answer

By equvilency near zero $\sin x\approx x$ we have

$$\lim_{x\to0^+}\frac{\sin x}{\sin \sqrt{x}}=\lim_{x\to0^+}\frac{x}{\sqrt{x}}=0$$
or
$$\lim_{x\to0^+}\frac{\sin x}{\sin \sqrt{x}}=\lim_{x\to0^+}\frac{\sin x}{x}\frac{\sqrt{x}}{\sin \sqrt{x}}.\sqrt{x}=1\times1\times0=0$$