To simplify the expression $\frac{\sqrt{7}}{\sqrt{3}}$, you can follow these steps:

Step 1: Use the property of square roots

We can simplify the fraction by using the rule $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. So, applying this to the given expression:

$\frac{\sqrt{7}}{\sqrt{3}} = \sqrt{\frac{7}{3}}$

Step 2: Rationalize the denominator

To rationalize the denominator (remove the square root from the denominator), multiply both the numerator and the denominator by $\sqrt{3}$:

$\frac{\sqrt{7}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{7} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

Step 3: Simplify

Since $\sqrt{3} \times \sqrt{3} = 3$, the expression becomes:

$\frac{\sqrt{7 \times 3}}{3} = \frac{\sqrt{21}}{3}$

Final Answer:

$\frac{\sqrt{7}}{\sqrt{3}} = \frac{\sqrt{21}}{3}$

Would you like more details on this or have any other questions? Here's a list of related topics:

1. What are the properties of square roots used in simplification?
2. How do you rationalize an expression with a square root in the denominator?
3. Can this method be applied to other irrational numbers?
4. How do you handle cube roots or higher powers in fractions?
5. What are some alternative ways to simplify square roots involving fractions?

Tip: When simplifying square roots, always check if the expression can be simplified further by factoring the number under the square root.