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Add. Write your answer in simplest form.\newline−25+95-2\sqrt{5} + 9\sqrt{5}

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Full solution

Q. Add. Write your answer in simplest form.\newline−25+95-2\sqrt{5} + 9\sqrt{5}
  1. Combine like terms: Combine the like terms −25-2\sqrt{5} and 959\sqrt{5}.\newlineSince both terms have the same radical part, 5\sqrt{5}, we can add the coefficients directly.\newline−25+95=(−2+9)5-2\sqrt{5} + 9\sqrt{5} = (-2 + 9)\sqrt{5}
  2. Simplify expression: Simplify the expression (−2+9)5(-2 + 9)\sqrt{5}. Perform the addition inside the parentheses. (−2+9)5=75(-2 + 9)\sqrt{5} = 7\sqrt{5} This is the simplest form since 77 and 55 are not perfect squares and have no common factors.

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