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To simplify the expression \(\frac{7}{\sqrt{2}}\) with a rational denominator, we need to "rationalize" the denominator. This is done by multiplying both the numerator and the denominator by \(\sqrt{2}\), the square root in the denominator. Here are the steps:

\[
\frac{7}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2}
\]

So, the expression simplifies to:

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

This is the simplest form with a rational denominator.

Would you like further clarification, or have any questions? Here are some related questions:

1. What is the process of rationalizing a denominator?
2. Why can't we leave a square root in the denominator?
3. How would this process change for higher-order roots, like cube roots?
4. What is an example of rationalizing a binomial denominator (e.g., \( \frac{1}{\sqrt{3} + 2} \))?
5. How can this concept be applied in complex fractions?

**Tip**: Rationalizing the denominator helps in standardizing the form of an expression, making it easier for further operations.

Express in simplest form with a rational denominator: 7/√2

Learn how to simplify the expression 7/√2 by rationalizing the denominator. This problem involves key algebraic concepts like simplifying radicals and rationalizing. Suitable for students in Grades 8-10.

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