https://file.aiquickdraw.com/mathbot/file/1728748237365p88kepe4.jpg

It appears the image you uploaded shows a mathematical expression, though it is currently upside down. Let me help you interpret it.

The expression in the image appears to be:

\[
\frac{5\sqrt{7}}{2}
\]

Along with the text: "Rationalize the denominator."

To rationalize the denominator of this expression, you would multiply both the numerator and denominator by \(\sqrt{7}\) to eliminate the square root in the denominator.

Let's perform the steps:

1. The original expression is:
   \[
   \frac{5\sqrt{7}}{2}
   \]
   
2. Multiply both the numerator and denominator by \(\sqrt{7}\):
   \[
   \frac{5\sqrt{7} \times \sqrt{7}}{2 \times \sqrt{7}} = \frac{5 \times 7}{2\sqrt{7}} = \frac{35}{2\sqrt{7}} 
   \]

Thus, the denominator is rationalized and becomes \(\sqrt{7}\).

Would you like further details on this? Here are 5 related questions to think about:

1. How do you rationalize a denominator with higher roots, like cube roots?
2. What if the denominator contains multiple terms, like \(\sqrt{3} + 1\)?
3. How do you simplify fractions after rationalizing the denominator?
4. Why is rationalizing the denominator an important technique in mathematics?
5. How do you apply rationalization in complex numbers?

**Tip**: Rationalizing the denominator is useful in making the expressions easier to work with, especially when adding or comparing fractions.

Rationalize the denominator of \( \frac{5\sqrt{7}}{2} \)

Learn how to rationalize the denominator of the fraction \( \frac{5\sqrt{7}}{2} \) with a step-by-step explanation. This solution covers key algebraic techniques including rationalization and simplification. Suitable for high school students in Grades 9-11.

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