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Add. Write your answer in simplest form.\newline−75+25-7\sqrt{5} + 2\sqrt{5}

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Full solution

Q. Add. Write your answer in simplest form.\newline−75+25-7\sqrt{5} + 2\sqrt{5}
  1. Combine like terms: Combine the like terms −75-7 \sqrt{5} and 252 \sqrt{5}. Identify the like terms which are the square root terms with the same radicand (number under the square root). −75+25=(−7+2)5-7 \sqrt{5} + 2 \sqrt{5} = (-7 + 2) \sqrt{5}
  2. Simplify expression: Simplify the expression (−7+2)5(-7 + 2) \sqrt{5}. Perform the addition within the parentheses. (−7+2)5=−55(-7 + 2) \sqrt{5} = -5 \sqrt{5}
  3. Write final answer: Write the final answer in simplest form.\newlineSince there are no further simplifications, the expression −55-5 \sqrt{5} is already in its simplest form.

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