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Add. Write your answer in simplest form.\newline−22+52-2\sqrt{2} + 5\sqrt{2}

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Full solution

Q. Add. Write your answer in simplest form.\newline−22+52-2\sqrt{2} + 5\sqrt{2}
  1. Combine like terms: Combine the like terms −22-2\sqrt{2} and 525\sqrt{2}. Since both terms have the same radical part, 2\sqrt{2}, we can add the coefficients directly. −22+52=(−2+5)2-2\sqrt{2} + 5\sqrt{2} = (-2 + 5)\sqrt{2}
  2. Simplify expression: Simplify the expression (−2+5)2(-2 + 5)\sqrt{2}. Perform the addition within the parentheses. (−2+5)2=32(-2 + 5)\sqrt{2} = 3\sqrt{2}

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