https://file.aiquickdraw.com/mathbot/file/17262287324141g14x6uk.jpg

The given expression is:

\[
\sqrt{20} + \sqrt{45}
\]

To simplify this expression, we can break down the square roots into their prime factors.

### Step 1: Simplifying \( \sqrt{20} \)
We know that:
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]

### Step 2: Simplifying \( \sqrt{45} \)
We know that:
\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
\]

### Step 3: Combining the terms
Now we have:
\[
\sqrt{20} + \sqrt{45} = 2\sqrt{5} + 3\sqrt{5}
\]

Since both terms have the same radical \( \sqrt{5} \), we can combine them:
\[
2\sqrt{5} + 3\sqrt{5} = (2 + 3)\sqrt{5} = 5\sqrt{5}
\]

Thus, the simplified expression is:

\[
5\sqrt{5}
\]

Would you like further details or have any other questions?

Here are 5 related questions to explore:
1. How do you simplify \( \sqrt{32} + \sqrt{50} \)?
2. What is the result of combining \( 4\sqrt{2} + 7\sqrt{2} \)?
3. How do you rationalize the denominator of \( \frac{1}{\sqrt{5}} \)?
4. What is the process to simplify \( \sqrt{72} + \sqrt{18} \)?
5. Can you explain how to add different square roots, like \( \sqrt{3} + \sqrt{12} \)?

**Tip**: When simplifying square roots, always factor numbers into perfect squares to make the process easier.

Learn how to simplify the radical expression √20 + √45 by breaking down the square roots into prime factors. This solution involves understanding how to factor perfect squares and combine like terms.

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