https://file.aiquickdraw.com/mathbot/file/1726090550512g6n194bx.jpg

The image contains a mathematical expression to be simplified. The expression is:

\[
\sqrt{5} + 6\sqrt{20}
\]

To simplify this, let's work through it step-by-step:

1. **Simplify the square root of 20**:
   \[
   \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
   \]

2. **Substitute this into the original expression**:
   \[
   \sqrt{5} + 6\sqrt{20} = \sqrt{5} + 6(2\sqrt{5}) = \sqrt{5} + 12\sqrt{5}
   \]

3. **Combine like terms**:
   \[
   \sqrt{5} + 12\sqrt{5} = 13\sqrt{5}
   \]

So, the simplified result is:
\[
13\sqrt{5}
\]

Would you like further details or have any questions? Here are five related questions to expand on this topic:

1. How do you simplify square roots involving products of numbers?
2. Can you always combine terms with square roots in an expression?
3. What is the process for rationalizing a denominator that contains a square root?
4. How would you handle expressions with cube roots, such as \( \sqrt[3]{20} \)?
5. How does factoring play a role in simplifying square roots?

**Tip:** Always look for perfect square factors when simplifying square roots to make the process easier.

Learn how to simplify the expression √5 + 6√20 by breaking down square roots and combining like terms. This step-by-step solution is suitable for students in Grades 8-10, covering radical simplification and algebraic techniques.

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