Simplify completely: 10radical63-9radical7 


Answer = 

 

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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.

Simplify completely: 10radical63-9radical7

Learn how to simplify the expression 10√63 - 9√7 with a detailed step-by-step guide. This problem covers key algebraic concepts, including simplification of radicals and combining like terms. Suitable for students in Grades 8-10.

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