Simplify square root of -16

Problem

√(,−16)

Solution

1. Identify the expression as the square root of a negative number, which requires the use of the imaginary unit i where i=√(,−1)

2. Rewrite the radicand as a product of a positive number and −1

√(,16⋅(−1))

3. Apply the product property of radicals, √(,a⋅b)=√(,a)⋅√(,b)

√(,16)⋅√(,−1)

4. Evaluate the square root of 16 and substitute i for √(,−1)

4⋅i

Final Answer

√(,−16)=4*i

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