https://file.aiquickdraw.com/mathbot/file/17259196888193xsoux4g.jpg

The image contains the mathematical expression:

\[
\sqrt{a b^3}
\]

This is the square root of the product of \(a\) and \(b^3\). To simplify this expression further, we can rewrite it as:

\[
\sqrt{a b^3} = \sqrt{a} \cdot \sqrt{b^3}
\]

Now, we simplify the square root of \(b^3\). Since \(b^3 = b^2 \cdot b\), we can apply the square root:

\[
\sqrt{b^3} = \sqrt{b^2 \cdot b} = b \cdot \sqrt{b}
\]

Therefore, the expression becomes:

\[
\sqrt{a b^3} = \sqrt{a} \cdot b \cdot \sqrt{b}
\]

This is the simplified form of the expression.

Would you like more details or have any questions about this?

Here are some related questions you can explore:
1. How do you simplify square roots of higher powers like \( b^5 \)?
2. What is the general rule for simplifying the square root of products?
3. Can square roots be simplified when one or more terms are negative?
4. How would this expression change if we were using cube roots instead of square roots?
5. How does the simplification of square roots apply in complex numbers?

**Tip**: Always break down the product inside the square root if the terms can be simplified individually.

Simplify the square root of the product of a and b cubed (√ab³).

Learn how to simplify the square root of the product of a and b cubed, using algebraic rules and properties of square roots. This tutorial covers key concepts such as the product rule for square roots and exponentiation.

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