Evaluate (-36)^(1/2)

Problem

(−36)(1/2)

Solution

1. Identify the expression as a square root, since raising a number to the power of 1/2 is equivalent to taking the square root.

(−36)(1/2)=√(,−36)

2. Apply the property of square roots of negative numbers, which states that √(,−a)=√(,a)⋅√(,−1) for any positive real number a

√(,−36)=√(,36)⋅√(,−1)

3. Substitute the imaginary unit i for √(,−1) and evaluate the square root of the positive real number.

√(,36)=6

√(,−1)=i

4. Multiply the results to find the final complex value.

6⋅i=6*i

Final Answer

(−36)(1/2)=6*i

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