Use the product rule to simplify the following expression.
√605x2

To simplify the expression \( \sqrt{605x^2} \) using the product rule, let's break it down step by step.

The product rule for square roots states:

\[
\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}
\]

For the given expression \( \sqrt{605x^2} \), we can treat this as the product of two terms:

\[
\sqrt{605x^2} = \sqrt{605} \cdot \sqrt{x^2}
\]

Now, we simplify each part:

- \( \sqrt{x^2} = x \)
- \( \sqrt{605} \) remains \( \sqrt{605} \) because 605 is not a perfect square.

Thus, the simplified expression is:

\[
\sqrt{605x^2} = x \sqrt{605}
\]

Would you like further details on this process or a different approach?

Here are 5 related questions to expand this topic:
1. How do you simplify square roots of larger numbers?
2. Can you simplify square roots that contain variables with exponents?
3. What is the process for rationalizing a square root in a fraction?
4. How do you use the product rule for other root types, like cube roots?
5. What happens when a negative number is under the square root?

**Tip:** Always check if the number under the square root can be factored into smaller numbers, as this may simplify the expression further.

Use the product rule to simplify the following expression: √605x²

Learn how to simplify the expression √605x² using the product rule for square roots. This solution demonstrates breaking down the square root into separate components and simplifying them step-by-step. Suitable for students in Grades 9-10.

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