The expression \( \sqrt{8x^3y^2} \) can be simplified as follows:

1. Break down the square root into its components:

\[
\sqrt{8x^3y^2} = \sqrt{8} \cdot \sqrt{x^3} \cdot \sqrt{y^2}
\]

2. Simplify each square root:

- \( \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \)
- \( \sqrt{x^3} = \sqrt{x^2 \cdot x} = x\sqrt{x} \)
- \( \sqrt{y^2} = y \)

3. Combine the simplified parts:

\[
\sqrt{8x^3y^2} = 2y \cdot x\sqrt{2x} = 2xy\sqrt{2x}
\]

So, the simplified form of \( \sqrt{8x^3y^2} \) is:

\[
2xy\sqrt{2x}
\]

Would you like further details or have any questions?

Here are 5 related questions you might explore:

1. How do you simplify expressions with higher powers under a square root?
2. What are the rules for simplifying square roots of fractions?
3. How do you simplify cube roots or higher degree roots?
4. What is the process for rationalizing the denominator involving square roots?
5. How do square roots behave when combined with exponents?

**Tip:** Always look for perfect squares when simplifying square roots to break them down easily!

Simplify the expression √(8x^3y^2) step-by-step by breaking it into components and applying the properties of square roots. This tutorial covers key algebraic concepts such as radicals, exponents, and simplification techniques, suitable for students in Grades 8-10.

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