Math Problem Statement

2**√6(43-3√**6)

Solution

To simplify the expression 26(4336)2\sqrt{6} \left( 4\sqrt{3} - 3\sqrt{6} \right), let's distribute 262\sqrt{6} to each term within the parentheses.

  1. Distribute 262\sqrt{6} to 434\sqrt{3}: 2643=863=8182\sqrt{6} \cdot 4\sqrt{3} = 8 \cdot \sqrt{6 \cdot 3} = 8\sqrt{18}

    Simplify 18\sqrt{18}: 18=9×2=32\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} So, 818=832=2428\sqrt{18} = 8 \cdot 3\sqrt{2} = 24\sqrt{2}

  2. Distribute 262\sqrt{6} to 36-3\sqrt{6}: 2636=666=636=66=362\sqrt{6} \cdot -3\sqrt{6} = -6 \cdot \sqrt{6 \cdot 6} = -6 \cdot \sqrt{36} = -6 \cdot 6 = -36

Now, combine the results: 2423624\sqrt{2} - 36

The simplified form of the expression is: 2423624\sqrt{2} - 36

Would you like further clarification or have any questions?

Here are five related questions to explore:

  1. How do you simplify expressions involving square roots?
  2. What are the properties of radicals that make simplification easier?
  3. How do you multiply and simplify expressions with multiple square roots?
  4. Can you add or subtract terms with different square roots?
  5. What are some techniques for recognizing factors under square roots?

Tip: When simplifying radicals, look for perfect square factors to make expressions easier to manage.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Simplification of Expressions with Square Roots

Formulas

Distributive property: a(b + c) = ab + ac
Square root multiplication: √a * √b = √(a * b)

Theorems

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Suitable Grade Level

Grades 9-10