Math Problem Statement

18√2+10√7-5√2-9√7

Solution

Let's simplify the expression:

182+107529718\sqrt{2} + 10\sqrt{7} - 5\sqrt{2} - 9\sqrt{7}

  1. Combine the terms with 2\sqrt{2}: (18252)=132(18\sqrt{2} - 5\sqrt{2}) = 13\sqrt{2}

  2. Combine the terms with 7\sqrt{7}: (10797)=17(10\sqrt{7} - 9\sqrt{7}) = 1\sqrt{7}

Now, putting it all together: 132+713\sqrt{2} + \sqrt{7}

So, the simplified expression is:

132+713\sqrt{2} + \sqrt{7}

Would you like further details or explanations on this? Here are five related questions to deepen your understanding:

  1. How do we combine terms with square roots?
  2. What is the importance of simplifying radical expressions?
  3. Can you simplify 35+753\sqrt{5} + 7\sqrt{5}?
  4. What happens if you try to add different radicals like 3+5\sqrt{3} + \sqrt{5}?
  5. Can square roots ever be simplified further, like 18\sqrt{18}?

Tip: When simplifying expressions involving square roots, only like terms (with the same radical part) can be combined.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radical Expressions

Formulas

Combining Like Terms with Square Roots

Theorems

None

Suitable Grade Level

Grades 8-10