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The problem asks to **rationalize the denominator** and **simplify** the expression:

\[
\frac{\sqrt{6}}{\sqrt{14}}
\]

### Step 1: Combine the square roots.
We can combine the square roots into one fraction under the radical:

\[
\frac{\sqrt{6}}{\sqrt{14}} = \sqrt{\frac{6}{14}}
\]

### Step 2: Simplify the fraction inside the square root.
The fraction \( \frac{6}{14} \) simplifies to \( \frac{3}{7} \):

\[
\sqrt{\frac{6}{14}} = \sqrt{\frac{3}{7}}
\]

### Step 3: Rationalize the denominator.
To rationalize the denominator, multiply both the numerator and denominator by \( \sqrt{7} \):

\[
\sqrt{\frac{3}{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{3} \times \sqrt{7}}{7} = \frac{\sqrt{21}}{7}
\]

### Final Answer:
The simplified and rationalized expression is:

\[
\frac{\sqrt{21}}{7}
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you rationalize a denominator with higher-degree roots (like cube roots)?
2. What is the process of simplifying radical expressions with variables involved?
3. Can you rationalize a denominator if both terms are under the radical?
4. What does it mean geometrically to rationalize the denominator?
5. How can you simplify expressions with multiple radical terms in both the numerator and denominator?

**Tip:** Always check if the fraction inside the square root can be simplified before rationalizing the denominator!

Rationalize the denominator and simplify: \( \frac{\sqrt{6}}{\sqrt{14}} \)

Learn how to rationalize the denominator and simplify the expression \( \frac{\sqrt{6}}{\sqrt{14}} \). This guide covers simplifying fractions under the square root and rationalizing the denominator. Suitable for Grades 8-10 students.

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