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Add. Write your answer in simplest form.\newline65+75-6\sqrt{5} + 7\sqrt{5}

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Q. Add. Write your answer in simplest form.\newline65+75-6\sqrt{5} + 7\sqrt{5}
  1. Combine Like Terms: Combine the like terms 65-6 \sqrt{5} and 757 \sqrt{5}. Since both terms have the same radical part, 5\sqrt{5}, we can combine them by adding their coefficients. 65+75=(6+7)5-6 \sqrt{5} + 7 \sqrt{5} = ( -6 + 7 ) \sqrt{5}
  2. Simplify Expression: Simplify the expression (6+7)5(-6 + 7) \sqrt{5}. Adding the coefficients 6-6 and 77 gives us 11, so the expression simplifies to: (6+7)5=15(-6 + 7) \sqrt{5} = 1 \sqrt{5} Since 11 times any number is the number itself, we can write this as: 15=51 \sqrt{5} = \sqrt{5}

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