It looks like you've uploaded a photo with several mathematical expressions involving square roots. Let's solve them step by step.

1. Expression 1: $5\sqrt{15} + 2\sqrt{15}$ Combine like terms: $(5 + 2)\sqrt{15} = 7\sqrt{15}$

2. Expression 2: $8\sqrt{30} - 2\sqrt{5} - 4\sqrt{30}$ Combine like terms: $(8 - 4)\sqrt{30} - 2\sqrt{5} = 4\sqrt{30} - 2\sqrt{5}$

3. Expression 3: $-\sqrt{12} + 3\sqrt{3}$ Simplify $\sqrt{12}$: $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$ So the expression becomes: $-2\sqrt{3} + 3\sqrt{3} = (3 - 2)\sqrt{3} = \sqrt{3}$

4. Expression 4: $5\sqrt{3} - \sqrt{27}$ Simplify $\sqrt{27}$: $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$ So the expression becomes: $5\sqrt{3} - 3\sqrt{3} = (5 - 3)\sqrt{3} = 2\sqrt{3}$

5. Expression 5: $2\sqrt{20} - 2\sqrt{45} + 3\sqrt{20}$ Simplify $\sqrt{20}$ and $\sqrt{45}$: $\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}, \quad \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$ Substituting these values in: $2(2\sqrt{5}) - 2(3\sqrt{5}) + 3(2\sqrt{5}) = 4\sqrt{5} - 6\sqrt{5} + 6\sqrt{5}$ Combine like terms: $(4 - 6 + 6)\sqrt{5} = 4\sqrt{5}$

6. Expression 6: $6\sqrt{5a} - 4\sqrt{5a}$ Combine like terms: $(6 - 4)\sqrt{5a} = 2\sqrt{5a}$

Would you like further clarification on any of these solutions? Feel free to ask any questions or request more examples. Here are some related questions you might find useful:

1. How do you simplify square roots involving variables?
2. Can you combine terms with different radicands?
3. How do you handle expressions with more than two terms involving square roots?
4. What are some tips for simplifying square roots in algebraic expressions?
5. How do you factor square roots for easier simplification?

Tip: Always simplify square roots before combining terms—this makes handling expressions much easier!