Evaluate square root of -75

Problem

√(,−75)

Solution

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

√(,−75)=√(,75)⋅√(,−1)

√(,−75)=√(,75)*i

2. Factor the radicand 75 into its prime factors to find the largest perfect square.

75=25⋅3

75=5⋅3

3. Simplify the radical by taking the square root of the perfect square 25

√(,75)*i=√(,25⋅3)*i

√(,75)*i=5√(,3)*i

Final Answer

√(,−75)=5*i√(,3)

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