Evaluate square root of -17

Problem

√(,−17)

Solution

1. Identify the expression as the square root of a negative number, which requires the use of the imaginary unit i

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

3. Substitute the definition of the imaginary unit, where i=√(,−1)

4. Simplify the expression by writing the result in terms of i Since 17 is a prime number, its square root cannot be simplified further into integers or simpler radicals.

Final Answer

√(,−17)=i√(,17)

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