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Add. Write your answer in simplest form.\newline−45+25-4\sqrt{5} + 2\sqrt{5}

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Full solution

Q. Add. Write your answer in simplest form.\newline−45+25-4\sqrt{5} + 2\sqrt{5}
  1. Combine like terms: Combine the like terms −45-4 \sqrt{5} and 252 \sqrt{5}. Since both terms have the same radical part, 5\sqrt{5}, we can add the coefficients directly. −45+25=(−4+2)5-4 \sqrt{5} + 2 \sqrt{5} = (-4 + 2) \sqrt{5}
  2. Simplify expression: Simplify the expression (−4+2)5(-4 + 2) \sqrt{5}. Perform the addition within the parentheses. (−4+2)5=(−2)5(-4 + 2) \sqrt{5} = (-2) \sqrt{5}
  3. Write final answer: Write the final answer in simplest form.\newlineSince there are no further simplifications, the final answer is −25-2 \sqrt{5}.

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