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Write sqrt(-90) in simplest radical form. Answer:

Write −90 \sqrt{-90} in simplest radical form.\newlineAnswer:

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Full solution

Q. Write −90 \sqrt{-90} in simplest radical form.\newlineAnswer:
  1. Express as product: Express −90\sqrt{-90} as the product of square roots and −1\sqrt{-1}.−90=−1×90=−1×90\sqrt{-90} = \sqrt{-1 \times 90} = \sqrt{-1} \times \sqrt{90}
  2. Use imaginary unit: Express −1\sqrt{-1} as the imaginary unit ii.\newline−1=i\sqrt{-1} = i
  3. Simplify by factoring: Simplify 90\sqrt{90} by factoring out perfect squares.90\sqrt{90} = 9×10\sqrt{9 \times 10} = 9\sqrt{9} ×\times 10\sqrt{10} = 3×103 \times \sqrt{10}
  4. Combine for complex number: Combine the results to express −90\sqrt{-90} as a complex number.−90=i×3×10=3i×10=3i10\sqrt{-90} = i \times 3 \times \sqrt{10} = 3i \times \sqrt{10} = 3i \sqrt{10}

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