Evaluate square root of -147

Problem

√(,−147)

Solution

1. Identify the imaginary unit by using the property √(,−a)=i√(,a) for any positive real number a

√(,−147)=i√(,147)

2. Factor the radicand to find the largest perfect square divisor.

147=49×3

3. Apply the product property of square roots, which states √(,a*b)=√(,a)√(,b)

i√(,49×3)=i√(,49)√(,3)

4. Simplify the square root of the perfect square.

√(,49)=7

5. Combine the terms into the final simplified form.

i×7×√(,3)=7*i√(,3)

Final Answer

√(,−147)=7*i√(,3)

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