Evaluate square root of -150

Problem

√(,−150)

Solution

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

√(,−150)=√(,150)⋅√(,−1)

√(,−150)=i√(,150)

2. Factor the radicand 150 to find the largest perfect square factor.

150=25⋅6

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

√(,150)=√(,25⋅6)

√(,150)=5√(,6)

4. Combine the simplified radical with the imaginary unit.

i*(5√(,6))=5*i√(,6)

Final Answer

√(,−150)=5*i√(,6)

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