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Express the radical using the imaginary unit, 
i.
Express your answer in simplified form.

+-sqrt(-70)=+-◻

Express the radical using the imaginary unit, i i .\newlineExpress your answer in simplified form.\newline±70=± \pm \sqrt{-70}= \pm \square

Full solution

Q. Express the radical using the imaginary unit, i i .\newlineExpress your answer in simplified form.\newline±70=± \pm \sqrt{-70}= \pm \square
  1. Express as product of square roots: Express ±70\pm\sqrt{-70} as the product of square roots and 1\sqrt{-1}.\newline±70=±170\pm\sqrt{-70} = \pm\sqrt{-1 \cdot 70}
  2. Recognize imaginary unit: Recognize that 1\sqrt{-1} is the imaginary unit ii.
    ±70=±1×70\pm\sqrt{-70} = \pm\sqrt{-1} \times \sqrt{70}
    = ±i×70\pm i \times \sqrt{70}
  3. Simplify square root of 7070: Simplify the square root of 7070 by looking for perfect square factors.\newline70=2×35=2×5×770 = 2 \times 35 = 2 \times 5 \times 7\newlineSince there are no perfect square factors in 7070, we cannot simplify 70\sqrt{70} further.
  4. Combine with imaginary unit: Combine the imaginary unit with the simplified radical. ±70=±i70\pm\sqrt{-70} = \pm i \cdot \sqrt{70}

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