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The expression you provided is:

\[
\sqrt{5x} \cdot \sqrt{15x^5}
\]

To simplify this, we can first combine the square roots under one radical, as follows:

\[
\sqrt{5x} \cdot \sqrt{15x^5} = \sqrt{(5x) \cdot (15x^5)}
\]

Now, multiply the terms inside the square root:

\[
= \sqrt{75x^6}
\]

Next, we simplify the square root:

\[
\sqrt{75x^6} = \sqrt{25 \cdot 3 \cdot x^6} = \sqrt{25} \cdot \sqrt{3} \cdot \sqrt{x^6}
\]

We know that \(\sqrt{25} = 5\) and \(\sqrt{x^6} = x^3\), so the expression becomes:

\[
5x^3 \cdot \sqrt{3}
\]

Thus, the simplified form of the expression is:

\[
5x^3\sqrt{3}
\]

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

Here are some related questions to deepen understanding:
1. How do you simplify square roots with variables?
2. What are the rules for multiplying square roots?
3. How do you simplify the square root of a product of numbers?
4. What is the process of rationalizing a square root?
5. How do you deal with fractional exponents?

**Tip:** Always break down square roots by separating perfect squares from non-perfect squares to simplify calculations.

Simplify the expression √5x · √15x^5

Learn how to simplify the expression √5x · √15x^5 by combining square roots and applying exponent rules. This solution covers radical properties and exponent manipulation, suitable for students in Grades 9-10.

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