Evaluate square root of -10

Problem

√(,−10)

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. Apply the property of square roots for negative numbers, √(,−a)=√(,−1)⋅√(,a)=i√(,a)

3. Substitute the value 10 into the property to get √(,−10)=i√(,10)

4. Determine if the radicand 10 can be simplified further. Since 10=2⋅5 has no perfect square factors, the radical is in simplest form.

Final Answer

√(,−10)=i√(,10)

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