Simplify root2( root6+2root2) minus2root3

Mathematics

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Answer

4

Step-by-step solution

5 steps

Let's simplify 2(6+22)−23\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3} step by step.

  1. Distribute 2\sqrt{2} into the parenthesis.

    2(6+22)=2×6+2×22\sqrt{2}(\sqrt{6} + 2\sqrt{2}) = \sqrt{2} \times \sqrt{6} + \sqrt{2} \times 2\sqrt{2}

  2. Simplify the products.

    2×6=12\sqrt{2} \times \sqrt{6} = \sqrt{12} 2×22=2×(2×2)=2×2=4\sqrt{2} \times 2\sqrt{2} = 2 \times (\sqrt{2} \times \sqrt{2}) = 2 \times 2 = 4

    So the expression becomes:

    12+4−23\sqrt{12} + 4 - 2\sqrt{3}

  3. Simplify 12\sqrt{12}.

    12=4×3=4×3=23\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}

  4. Substitute the simplified term back into the expression.

    23+4−232\sqrt{3} + 4 - 2\sqrt{3}

  5. Combine like terms.

    (23−23)+4=0+4=4(2\sqrt{3} - 2\sqrt{3}) + 4 = 0 + 4 = 4

    The final answer is 4.

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