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Add. Write your answer in simplest form.\newline102+72-10\sqrt{2} + 7\sqrt{2}

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Q. Add. Write your answer in simplest form.\newline102+72-10\sqrt{2} + 7\sqrt{2}
  1. Combine like terms: Combine the like terms 102-10 \sqrt{2} and 727 \sqrt{2}. Identify the like terms that can be combined by adding their coefficients. 102+72=(10+7)2-10 \sqrt{2} + 7 \sqrt{2} = (-10 + 7) \sqrt{2}
  2. Simplify expression: Simplify the expression (10+7)2(-10 + 7) \sqrt{2}.\newlineCalculate the sum of the coefficients and multiply by the common radical.\newline(10+7)2=32(-10 + 7) \sqrt{2} = -3 \sqrt{2}
  3. Check for simplification: Check for any possible simplification.\newlineSince 3-3 is the simplest form of the coefficient and 2\sqrt{2} cannot be simplified further, the expression is already in its simplest form.\newline32-3 \sqrt{2} is the final answer.

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