Evaluate square root of -54

Problem

√(,−54)

Solution

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

√(,−54)=√(,54)⋅√(,−1)

√(,−54)=√(,54)*i

2. Factor the radicand 54 into its prime factors to find the largest perfect square divisor.

54=9⋅6

54=3⋅6

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

√(,54)*i=√(,9⋅6)*i

√(,54)*i=3√(,6)*i

Final Answer

√(,−54)=3*i√(,6)

Want more problems? Check here!