https://file.aiquickdraw.com/mathbot/file/1728549356598xz1lwi0d.jpg

The expression provided in the image is:

\[
\frac{\sqrt{7}}{\sqrt{6}}
\]

To rationalize the denominator, we need to eliminate the square root in the denominator. We do this by multiplying both the numerator and the denominator by \(\sqrt{6}\), as follows:

\[
\frac{\sqrt{7}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{\sqrt{7} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}} = \frac{\sqrt{42}}{6}
\]

Thus, the rationalized form of the expression is:

\[
\frac{\sqrt{42}}{6}
\]

This is the simplified expression with a rationalized denominator.

Would you like any further clarification or details on this?

Here are 5 related questions you might consider:
1. What is the process for rationalizing more complex denominators?
2. How would this change if the expression involved cube roots instead of square roots?
3. Can you explain why we multiply by the denominator's square root to rationalize?
4. What other types of irrational denominators might require a different approach to rationalize?
5. How does rationalizing affect the numerical value of the expression?

**Tip:** When rationalizing denominators, always check if the resulting expression can be simplified further.

Rationalize the denominator and simplify: \(\frac{\sqrt{7}}{\sqrt{6}}\)

Learn how to rationalize the denominator and simplify the expression \(\frac{\sqrt{7}}{\sqrt{6}}\). This step-by-step solution covers the multiplication of square roots and simplifying radical expressions, suitable for high school students (Grades 9-12).

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