To simplify the expression \( 6 \frac{\sqrt{20}}{\sqrt{5}} \):

1. **Simplify the fraction inside the radical:**

   \[
   \frac{\sqrt{20}}{\sqrt{5}} = \sqrt{\frac{20}{5}}
   \]

2. **Simplify the fraction under the radical:**

   \[
   \frac{20}{5} = 4
   \]

3. **Simplify the square root:**

   \[
   \sqrt{4} = 2
   \]

4. **Multiply by 6:**

   \[
   6 \times 2 = 12
   \]

So, the simplified form of the expression is:

\[
6 \frac{\sqrt{20}}{\sqrt{5}} = 12
\]

Would you like more details or have any questions?

Here are 8 related questions you might find interesting:
1. How do you simplify \(\sqrt{\frac{a}{b}}\)?
2. What are the properties of square roots?
3. How do you multiply and divide square roots?
4. Can you explain the steps to rationalize the denominator?
5. How do you simplify \(\sqrt{50} / \sqrt{2}\)?
6. What is the simplified form of \(5 \sqrt{18} / \sqrt{3}\)?
7. How do you simplify \( \frac{3 \sqrt{45}}{5 \sqrt{5}} \)?
8. How do you handle square roots in algebraic fractions?

**Tip:** When simplifying radicals, always look to simplify the fraction under the radical first, if possible, to make the calculations easier.

Learn how to simplify the expression 6 sqrt(20) / sqrt(5) step-by-step. This problem involves radicals and fraction simplification. Suitable for high school students studying algebra and advanced mathematics.

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