https://file.aiquickdraw.com/mathbot/file/1727435961223icyqcp76.jpg

The expression in the image appears to be:

\[
\left( \sqrt{45} - \sqrt{5} \right)^2
\]

Let's break this down and simplify it:

1. **Simplify each square root:**
   - \(\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}\)
   - \(\sqrt{5}\) stays as it is.

So the expression becomes:

\[
\left( 3\sqrt{5} - \sqrt{5} \right)^2
\]

2. **Factor out the common term \(\sqrt{5}\):**

\[
\left( 3\sqrt{5} - \sqrt{5} \right) = \sqrt{5}(3 - 1) = 2\sqrt{5}
\]

3. **Square the result:**

\[
\left( 2\sqrt{5} \right)^2 = 4 \times 5 = 20
\]

So, the simplified value of the expression is:

\[
\boxed{20}
\]

Would you like more details on any part of the process?

Here are 5 related questions to help reinforce this concept:
1. How do you simplify square roots of non-perfect squares like \(\sqrt{45}\)?
2. What is the significance of factoring out common terms in expressions?
3. How would the solution change if the expression were \(\left( \sqrt{45} + \sqrt{5} \right)^2\)?
4. What other forms can the distributive property take when simplifying such expressions?
5. How does squaring affect terms involving square roots?

**Tip:** When squaring binomials involving square roots, always simplify the square roots first before proceeding with expansion or squaring.

Simplify the expression (sqrt(45) - sqrt(5))^2

Learn how to simplify the expression (sqrt(45) - sqrt(5))^2. This solution involves simplifying square roots and applying the distributive property. Suitable for students in Grades 9-10.

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