Simplify: \[-10sqrt(7)-9sqrt(2)-8sqrt(7)+7sqrt(2)\] Choose 1 answer: A \[-2sqrt(7)-16sqrt(2)\] B \[-18sqrt(7)-16sqrt(2)\] C \[-18sqrt(7)-2sqrt(2)\] D \[-2sqrt(7)-2sqrt(2)\] Related content

Mathematics

ScanSolve AI Answer

Answer

−187−22-18\sqrt{7}-2\sqrt{2}

Step-by-step solution

3 steps

To simplify the expression, we combine like terms. Like terms are those that have the same radical part.

  1. Identify and combine terms with 7\sqrt{7}

    The terms with 7\sqrt{7} are −107-10\sqrt{7} and −87-8\sqrt{7}.
    Combine their coefficients:
    −107−87=(−10−8)7=−187-10\sqrt{7} - 8\sqrt{7} = (-10 - 8)\sqrt{7} = -18\sqrt{7}

  2. Identify and combine terms with 2\sqrt{2}

    The terms with 2\sqrt{2} are −92-9\sqrt{2} and +72+7\sqrt{2}.
    Combine their coefficients:
    −92+72=(−9+7)2=−22-9\sqrt{2} + 7\sqrt{2} = (-9 + 7)\sqrt{2} = -2\sqrt{2}

  3. Combine the simplified terms

    Add the results from Step 1 and Step 2:
    −187−22-18\sqrt{7} - 2\sqrt{2}

    Comparing this result with the given options, it matches option C.

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