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The expression you provided is:

\[
\sqrt{25x^2y^2}
\]

To simplify this expression, we can break it down as follows:

\[
\sqrt{25x^2y^2} = \sqrt{25} \cdot \sqrt{x^2} \cdot \sqrt{y^2}
\]

Now, simplify each part:

1. \(\sqrt{25} = 5\)
2. \(\sqrt{x^2} = x\) (assuming \(x \geq 0\))
3. \(\sqrt{y^2} = y\) (assuming \(y \geq 0\))

So, the simplified form of the expression is:

\[
5xy
\]

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

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Here are five related questions to consider:

1. How would the simplification change if \(x\) or \(y\) could be negative?
2. What if the expression under the square root was \(\sqrt{49x^4y^4}\)?
3. How do you simplify \(\sqrt{x^4 + y^4}\)?
4. Can you apply the same process to simplify \(\sqrt{100x^6y^2}\)?
5. What are the rules for simplifying square roots of products and quotients?

**Tip:** Always consider the domain (possible values) of the variables when simplifying expressions involving square roots, as this can affect the final form.

Simplify the square root expression \(\sqrt{25x^2y^2}\).

Learn how to simplify square root expressions like \(\sqrt{25x^2y^2}\). This step-by-step solution covers the use of radical properties and assumptions about variables, ideal for students in Grades 8-10.

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