Evaluate square root of -48

Problem

√(,−48)

Solution

1. Identify the negative radicand and rewrite the expression using the imaginary unit i where i=√(,−1)

√(,−48)=√(,−1⋅48)

√(,−48)=i√(,48)

2. Factor the number 48 to find the largest perfect square divisor.

48=16⋅3

3. Apply the product property of square roots to separate the perfect square.

i√(,48)=i√(,16⋅3)

i√(,48)=i√(,16)⋅√(,3)

4. Simplify the square root of the perfect square.

√(,16)=4

i⋅4⋅√(,3)=4*i√(,3)

Final Answer

√(,−48)=4*i√(,3)

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