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

+-sqrt(-20)=+-◻

Express the radical using the imaginary unit, i i .\newlineExpress your answer in simplified form.\newline±20=± \pm \sqrt{-20}= \pm \square

Full solution

Q. Express the radical using the imaginary unit, i i .\newlineExpress your answer in simplified form.\newline±20=± \pm \sqrt{-20}= \pm \square
  1. Rephrasing and recognizing: First, let's rephrase the "Express the radical using the imaginary unit, ii, and simplify the expression ±20\pm\sqrt{-20}."
  2. Separating the square root: Recognize that the square root of a negative number involves the imaginary unit ii, where i2=1i^2 = -1. We can express ±20\pm\sqrt{-20} as ±1×20\pm\sqrt{-1 \times 20}.
  3. Replacing 1\sqrt{-1} with ii: Separate the square root of the product into the product of square roots, knowing that ab=ab\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}. This gives us ±120\pm\sqrt{-1} \cdot \sqrt{20}.
  4. Simplifying 20\sqrt{20}: Replace 1\sqrt{-1} with ii, since they are equivalent. This transforms the expression into ±i20\pm i \cdot \sqrt{20}.
  5. Taking the square root of 44: Simplify 20\sqrt{20} by factoring it into 4×5\sqrt{4 \times 5}, since 44 is a perfect square and its square root can be easily calculated.
  6. Combining constants outside the radical: Take the square root of 44, which is 22, and bring it outside the radical. This leaves us with ±i25\pm i \cdot 2 \cdot \sqrt{5}.
  7. Combining constants outside the radical: Take the square root of 44, which is 22, and bring it outside the radical. This leaves us with ±i25\pm i \cdot 2 \cdot \sqrt{5}.Combine the constants outside the radical to simplify the expression. This results in ±2i5\pm 2i \cdot \sqrt{5}.

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