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Multiply. Write your answer in simplest form. \newline5(10−2)\sqrt{5}(10 - \sqrt{2})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline5(10−2)\sqrt{5}(10 - \sqrt{2})
  1. Distribute 5\sqrt{5}: Distribute 5\sqrt{5} across the terms inside the parentheses.5(10−2)=5×10−5×2\sqrt{5}(10 - \sqrt{2}) = \sqrt{5} \times 10 - \sqrt{5} \times \sqrt{2}
  2. Multiply by 1010: Multiply 5\sqrt{5} by 1010.5×10=105\sqrt{5} \times 10 = 10\sqrt{5}
  3. Multiply by 2\sqrt{2}: Multiply 5\sqrt{5} by 2\sqrt{2}.5×2=5×2=10\sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10}
  4. Combine results: Combine the two results to get the final expression. 105−1010\sqrt{5} - \sqrt{10}
  5. Check for simplification: Check if the expression can be simplified further.\newlineSince there are no like radical terms, the expression is already in simplest form.

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