https://file.aiquickdraw.com/mathbot/file/17262338677404y1aouml.jpg

The expression shown in the image is:

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

Let's simplify each square root term:

1. \(\sqrt{20}\):
   \[
   \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
   \]

2. \(\sqrt{45}\):
   \[
   \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
   \]

Now add them together:
\[
2\sqrt{5} + 3\sqrt{5} = 5\sqrt{5}
\]

Thus, the simplified result is:
\[
\boxed{5\sqrt{5}}
\]

Would you like more details on this, or do you have any further questions?

Here are 5 related questions to expand your understanding:
1. How can you simplify expressions involving other square roots, like \(\sqrt{50}\) or \(\sqrt{80}\)?
2. What are the properties of square roots that allow us to factor terms like \(\sqrt{20}\) and \(\sqrt{45}\)?
3. Can you apply this simplification method to cube roots, such as \(\sqrt[3]{54}\)?
4. How do you rationalize square roots in the denominator of a fraction?
5. What happens when you add or subtract square roots with different radicands, such as \(\sqrt{7} + \sqrt{5}\)?

**Tip**: When simplifying square roots, always look for perfect squares (like 4, 9, 16) that are factors of the number under the square root.

Learn how to simplify the expression √20 + √45 by breaking down square roots into their prime factors and combining like terms. This solution involves key algebraic concepts and properties of square roots, suitable for students in Grades 7-9.

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