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Write sqrt(-250) in simplest radical form. Answer:

Write −250 \sqrt{-250} in simplest radical form.\newlineAnswer:

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Full solution

Q. Write −250 \sqrt{-250} in simplest radical form.\newlineAnswer:
  1. Express as product of square roots: Express −250\sqrt{-250} as the product of square roots and −1\sqrt{-1}.−250=−1×250=−1×250\sqrt{-250} = \sqrt{-1 \times 250} = \sqrt{-1} \times \sqrt{250}
  2. Recognize imaginary unit: Recognize that −1\sqrt{-1} is the imaginary unit ii.−250\sqrt{-250} = −1\sqrt{-1} * 250\sqrt{250} = ii * 250\sqrt{250}
  3. Simplify by factoring perfect squares: Simplify 250\sqrt{250} by factoring out perfect squares.\newline250\sqrt{250} \newline= 25×10\sqrt{25 \times 10}\newline= 25\sqrt{25} ×\times 10\sqrt{10}\newline= 5×105 \times \sqrt{10}
  4. Combine with simplified radical: Combine the imaginary unit ii with the simplified radical.i⋅250i \cdot \sqrt{250} =i⋅5⋅10= i \cdot 5 \cdot \sqrt{10} =5i⋅10= 5i \cdot \sqrt{10}

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