To simplify the expression \( \frac{7}{\sqrt{12}} \), you can follow these steps:

1. **Rationalize the denominator** by multiplying both the numerator and the denominator by \( \sqrt{12} \) to eliminate the square root from the denominator:

\[
\frac{7}{\sqrt{12}} \times \frac{\sqrt{12}}{\sqrt{12}} = \frac{7\sqrt{12}}{12}
\]

2. **Simplify the square root** in the numerator. Notice that \( \sqrt{12} \) can be simplified further because \( 12 = 4 \times 3 \), and \( \sqrt{4} = 2 \):

\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]

So, substitute \( \sqrt{12} \) with \( 2\sqrt{3} \):

\[
\frac{7\sqrt{12}}{12} = \frac{7 \times 2\sqrt{3}}{12} = \frac{14\sqrt{3}}{12}
\]

3. **Simplify the fraction** \( \frac{14}{12} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

\[
\frac{14\sqrt{3}}{12} = \frac{7\sqrt{3}}{6}
\]

So, the simplified form of \( \frac{7}{\sqrt{12}} \) is \( \frac{7\sqrt{3}}{6} \).

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would you simplify \( \frac{5}{\sqrt{8}} \)?
2. What is the process to rationalize a denominator involving cube roots?
3. How can \( \frac{9}{\sqrt{20}} \) be simplified?
4. Can you express \( \frac{3}{\sqrt{2}} \) in a simplified form?
5. How does rationalizing the denominator affect the value of the expression?

**Tip:** Always look for factors of the radicand (the number inside the square root) that are perfect squares, as this can simplify your calculations when rationalizing the denominator.

Learn how to simplify the expression \( \frac{7}{\sqrt{12}} \) with detailed step-by-step instructions. Explore rationalizing denominators, simplifying square roots, and fraction simplification techniques. Ideal for students in Grades 9-12.

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