1. **Stating the problem:** Simplify the expression $$\frac{\sqrt{105}}{\sqrt{21}}$$ and verify if it equals $$\sqrt{5}$$. 2. **Formula and rules:** Recall that $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$ for positive numbers $$a$$ and $$b$$. 3. **Apply the formula:** $$\frac{\sqrt{105}}{\sqrt{21}} = \sqrt{\frac{105}{21}}$$ 4. **Simplify the fraction inside the square root:** $$\frac{105}{21} = \cancel{\frac{105}{21}}^{5}$$ (since $$21 \times 5 = 105$$) 5. **Rewrite the expression:** $$\sqrt{5}$$ 6. **Conclusion:** The original expression simplifies exactly to $$\sqrt{5}$$, so the equality $$\frac{\sqrt{105}}{\sqrt{21}} = \sqrt{5}$$ is correct.