Subjects algebra

Sqrt Negative Cb5C2B

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Sqrt Negative Cb5C2B


1. The problem is to rewrite the expression $\sqrt{-30}$ as a complex number and simplify all radicals. 2. Recall that the imaginary unit $i$ is defined as $i = \sqrt{-1}$. 3. Using this, we can rewrite $\sqrt{-30}$ as $\sqrt{30 \times -1} = \sqrt{30} \times \sqrt{-1} = \sqrt{30} \times i$. 4. Since $\sqrt{30}$ cannot be simplified further (30 factors as $2 \times 3 \times 5$, none are perfect squares), the simplified form is $i \sqrt{30}$. 5. Therefore, the expression $\sqrt{-30}$ rewritten as a complex number is $$i \sqrt{30}$$.