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.