Here's the set of exercises you've shared, centered around simplifying square roots and performing arithmetic operations with them. Let’s provide the solutions step by step.

### 1. Tính

a) \(\sqrt{27.75} = \sqrt{27.75} = \sqrt{27 \cdot 1 + 0.75} = \sqrt{27} + \sqrt{0.75} \approx 5.27\)

b) \(\sqrt{200.18} \approx \sqrt{200} + \sqrt{0.18} \approx 14.14\)

c) \(\sqrt{160.12} \approx 12.65\)

d) \(\sqrt{3 \cdot 6.25} = \sqrt{18.75} \approx 4.33\)

### 2. Tính

a) \(\sqrt{45} \cdot \sqrt{180} = \sqrt{8100} = 90\)

b) \(\sqrt{7} \cdot \sqrt{105} = \sqrt{735} \approx 27.13\)

c) \(\sqrt{250} \cdot \sqrt{0.9} = \sqrt{225} = 15\)

### 3. Tính

a) \(\sqrt{2} \approx 1.414\)

b) \(\sqrt{\frac{1}{2}} \cdot \sqrt{\frac{3}{7}} \cdot \sqrt{12} = \sqrt{\frac{36}{14}} = \sqrt{2.57} \approx 1.6\)

c) \(\sqrt{72} \cdot \sqrt{50} = \sqrt{3600} = 60\)

### 4. Tính

a) \(\sqrt{\frac{2}{3} + \frac{50}{3}} - \sqrt{24} = \sqrt{17/3} - 4.9\)

b) \(\sqrt{3} + \sqrt{5} \cdot \sqrt{2} \)

### 5. Tính

a) \(\sqrt{553.77} \approx 23.5\)

b) \(\sqrt{\frac{1}{8}} \cdot \sqrt{2} \cdot \sqrt{125} = \sqrt{15.625} \approx 3.95\)

c) \(2 \cdot ( \sqrt{2.5} + (1 + 2)^{2} - 2 \sqrt{6})\)

### 6. Khai triển biểu thức sau

a) \((\sqrt{7} + \sqrt{3})^{3}\)

b) \((\sqrt{8} - \sqrt{2})^{2}\)

c) \((\sqrt{x} + 2) \cdot (\sqrt{x} - 3)\)

You can expand each expression step by step, applying the properties of square roots along with algebraic identities as necessary. If you would like more detailed solutions or further calculations, please let me know!