https://file.aiquickdraw.com/mathbot/file/1725811118046wzmh7djc.jpg

The problem shown in the image asks you to "Rationalize the denominator" for the expression:

\[
\frac{1}{\sqrt{x}}
\]

To rationalize the denominator, we need to eliminate the square root in the denominator by multiplying both the numerator and the denominator by \(\sqrt{x}\):

\[
\frac{1}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}} = \frac{\sqrt{x}}{x}
\]

Now, the denominator is rationalized, and the final expression is:

\[
\frac{\sqrt{x}}{x}
\]

Would you like further details or explanations about any of the steps?

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Here are 5 related questions:
1. How do you rationalize a denominator involving cube roots?
2. Can the same process be applied to rationalize \(\frac{1}{\sqrt{2x}}\)?
3. Why is rationalizing the denominator important in simplifying expressions?
4. How do you rationalize denominators with sums involving radicals?
5. What happens when you rationalize the denominator of complex fractions with radicals?

**Tip:** Always check for any opportunity to simplify further after rationalizing the denominator!

Rationalize the denominator of the expression \( \frac{1}{\sqrt{x}} \).

This guide walks through the process of rationalizing the denominator for the expression \( \frac{1}{\sqrt{x}} \). Learn how to eliminate radicals from the denominator by multiplying by \( \sqrt{x} \), with a clear, step-by-step solution. Suitable for students in Grades 8-10.

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