Evaluate square root of -343

Problem

√(,−343)

Solution

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

√(,−343)=√(,343)⋅√(,−1)

√(,−343)=i√(,343)

2. Factor the number 343 to find its prime factorization. Since 7=343 we can write it as a product of a perfect square and a factor.

343=49⋅7

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

√(,343)=√(,49⋅7)

√(,343)=7√(,7)

4. Combine the simplified radical with the imaginary unit to find the final value.

i*(7√(,7))=7*i√(,7)

Final Answer

√(,−343)=7*i√(,7)

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