Simplify square root of -64

Problem

√(,−64)

Solution

1. Identify the square root of a negative number by using the imaginary unit i where i=√(,−1)

2. Rewrite the expression as the product of the square root of the positive number and the square root of −1

√(,−64)=√(,64⋅(−1))

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

√(,64⋅(−1))=√(,64)⋅√(,−1)

4. Evaluate the square root of 64 and substitute i for √(,−1)

√(,64)⋅√(,−1)=8⋅i

Final Answer

√(,−64)=8*i

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