Rút gọn biểu thức

To simplify the expressions in the image, follow these steps for each item:

1. **Expression**: \(\sqrt{0.36a^2}, a < 0\)
- Simplification: \(0.6|a|\) (since \(a\) is negative, \(|a| = -a\))

2. **Expression**: \(\sqrt{a^4(3-a)^2}, a > 0\)
- Simplification: \(a^2(3-a)\)

3. **Expression**: \(\sqrt{27 \cdot 48 (1-a)^2}, a > 1\)
- Simplification: \(12\sqrt{3} (1-a)\)

4. **Expression**: \(\sqrt{\frac{2a}{3}}, \sqrt{\frac{3a}{8}}, a > 1\)
- Simplification: Combine: \(\sqrt{\frac{6a}{24}} = \frac{\sqrt{a}}{2\sqrt{2}}\)

5. **Expression**: \(\sqrt{13a}, \sqrt{\frac{5^2}{9}}, a > 0\)
- Simplification: \(\sqrt{13a} \cdot \frac{5}{3} = \frac{5\sqrt{13a}}{3}\)

6. **Expression**: \(\sqrt{5a}, \sqrt{459} - 3a, a > 0\)
- Simplification: \(\sqrt{5a} + \sqrt{459} - 3a\)

7. **Expression**: \(\frac{\sqrt{2^2b^4}}{54}\)
- Simplification: \(\frac{2b^2}{54} = \frac{b^2}{27}\)

8. **Expression**: \(\frac{\sqrt{27a}}{\sqrt{39}}, a > 0\)
- Simplification: \(\frac{3\sqrt{3a}}{\sqrt{39}} = \frac{3\sqrt{3a}}{3\sqrt{13}} = \frac{\sqrt{3a}}{\sqrt{13}}\)

9. **Expression**: \(\frac{y}{x} \cdot \sqrt{\frac{x}{y^4}}, x < 0, y \neq 0\)
- Simplification: \(\frac{y \sqrt{x}}{xy^2} = \frac{\sqrt{x}}{y}\)

10. **Expression**: \(\cdots, 2y^2\)
- Requires more context to simplify, but the pattern follows.

These steps illustrate how to perform the simplifications. Each expression can be handled similarly, extracting roots and simplifying fractions when applicable.