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−4\sqrt{-4}

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Full solution

Q. −4\sqrt{-4}
  1. Evaluate Negative Square Root: Evaluate the square root of a negative number. The square root of a negative number is not a real number; it involves an imaginary unit ' extit{i}' where i2=−1i^2 = -1. Therefore, −4\sqrt{-4} can be written as (−1×4)\sqrt{(-1 \times 4)}.
  2. Simplify Using Imaginary Unit: Simplify the expression using the imaginary unit.\newlineSince −1\sqrt{-1} is equal to 'ii' and 4\sqrt{4} is equal to 22, we can rewrite −4\sqrt{-4} as 2i2i.
  3. Check for Errors: Check for any mathematical errors.\newlineThere are no mathematical errors in the previous steps. The expression has been simplified correctly using the properties of square roots and imaginary numbers.

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