To simplify the expression $10\sqrt{63} - 9\sqrt{7}$, we need to factor the square roots if possible.

1. Start by simplifying $\sqrt{63}$:

   • $\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}$.

2. Substitute this back into the expression: $10\sqrt{63} - 9\sqrt{7} = 10 \times 3\sqrt{7} - 9\sqrt{7} = 30\sqrt{7} - 9\sqrt{7}$

3. Combine like terms: $30\sqrt{7} - 9\sqrt{7} = (30 - 9)\sqrt{7} = 21\sqrt{7}$

So, the simplified expression is $\boxed{21\sqrt{7}}$.

Would you like any further details or have any questions?

Here are 5 related questions:

1. How do you simplify expressions with different square roots?
2. What is the general method to factor square roots?
3. Can you simplify $\sqrt{28} - 3\sqrt{7}$?
4. What happens when you have to simplify an expression like $5\sqrt{45} + 2\sqrt{20}$?
5. How can you simplify $4\sqrt{48} + \sqrt{75}$?

Tip: When simplifying square roots, always check if the number inside the square root can be factored into a perfect square.