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If x≥ 0 and y > 0 are real numbers, simplify the following expression

The expression in the image is:

\[
\sqrt{5xy} - 3\sqrt{xy}
\]

We can simplify this by factoring out the common term \(\sqrt{xy}\).

### Step-by-step simplification:
1. Factor out \(\sqrt{xy}\) from both terms:
   \[
   \sqrt{5xy} - 3\sqrt{xy} = \sqrt{xy} \left( \sqrt{5} - 3 \right)
   \]

So, the simplified expression is:
\[
\boxed{\sqrt{xy} \left( \sqrt{5} - 3 \right)}
\]

Would you like further clarification or details on this process?

### Relative questions:
1. How would you simplify a similar expression like \(\sqrt{7ab} - 2\sqrt{ab}\)?
2. What happens if the variables in the expression have negative values?
3. How do you simplify more complex square root expressions with multiple terms?
4. Can you apply the same factoring technique to cube roots or higher?
5. How do you handle square roots of sums, like \(\sqrt{x + y}\)?

### Tip:
When simplifying expressions with square roots, always look for common factors that can be factored out to reduce complexity.

If x≥ 0 and y > 0 are real numbers, simplify the following expression: \( \sqrt{5xy} - 3\sqrt{xy} \).

Learn how to simplify expressions involving square roots and factoring, such as \( \sqrt{5xy} - 3\sqrt{xy} \). This problem helps students understand the concept of factoring and applying square root properties. Suitable for students in Grades 7-10.

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