Evaluate square root of -45

Problem

√(,−45)

Solution

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

√(,−45)=√(,45)⋅√(,−1)

√(,−45)=√(,45)*i

2. Factor the radicand 45 into its prime factors to find the largest perfect square.

45=9⋅5

45=3⋅5

3. Simplify the radical by taking the square root of the perfect square 9

√(,45)*i=√(,9⋅5)*i

√(,45)*i=3√(,5)*i

Final Answer

√(,−45)=3*i√(,5)

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