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Write sqrt(-20) in simplest radical form. Answer:

Write −20 \sqrt{-20} in simplest radical form.\newlineAnswer:

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Full solution

Q. Write −20 \sqrt{-20} in simplest radical form.\newlineAnswer:
  1. Express as product: Express −20\sqrt{-20} as the product of square roots and −1\sqrt{-1}.\newline−20=−1×20\sqrt{-20} = \sqrt{-1 \times 20}
  2. Recognize imaginary unit: Recognize that −1\sqrt{-1} is the imaginary unit ii.−20=−1×20\sqrt{-20} = \sqrt{-1} \times \sqrt{20}=i×20= i \times \sqrt{20}
  3. Simplify radical: Simplify 20\sqrt{20} by factoring out the perfect square.\newline20=4×5\sqrt{20} = \sqrt{4 \times 5}\newline=4×5= \sqrt{4} \times \sqrt{5}\newline=2×5= 2 \times \sqrt{5}
  4. Combine imaginary unit: Combine the imaginary unit with the simplified radical. \newlinei⋅20=i⋅2⋅5i \cdot \sqrt{20} = i \cdot 2 \cdot \sqrt{5}\newline=2i⋅5= 2i \cdot \sqrt{5}

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