Express in simplest form with a rational denominator.

start fraction, 2, divided by, square root of, 3, end square root, end fraction

3​2​

To express the fraction \( \frac{2}{\sqrt{3}} \) with a rational denominator, we need to rationalize the denominator by multiplying both the numerator and the denominator by \( \sqrt{3} \).

\[
\frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{(\sqrt{3})^2}
\]

Since \( (\sqrt{3})^2 = 3 \), we get:

\[
\frac{2\sqrt{3}}{3}
\]

So, the expression in its simplest form with a rational denominator is:

\[
\frac{2\sqrt{3}}{3}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you rationalize \( \frac{5}{\sqrt{2}} \)?
2. What is the process to rationalize \( \frac{7}{\sqrt{5}} \)?
3. Can you simplify \( \frac{4}{\sqrt{6}} \)?
4. How would you rationalize \( \frac{3}{\sqrt{7}} \)?
5. What is the simplified form of \( \frac{1}{\sqrt{8}} \)?

**Tip:** When rationalizing denominators, multiply by the same square root to avoid changing the value of the fraction.

Express in simplest form with a rational denominator: \( \frac{2}{\sqrt{3}} \)

Learn how to simplify the fraction \( \frac{2}{\sqrt{3}} \) by rationalizing the denominator. This step-by-step solution explains how to multiply by the square root to eliminate radicals in the denominator. Ideal for students in Grades 8-10.

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