Subjects algebra

Simplify Radical 7C2F04

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1. The problem is to simplify $\sqrt{-18}$ into simplest radical form. 2. Recall that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and $\sqrt{-1} = i$ where $i$ is the imaginary unit. 3. We can write $\sqrt{-18}$ as $\sqrt{-1 \times 18}$. 4. Using the property of square roots, this becomes $\sqrt{-1} \times \sqrt{18} = i \times \sqrt{18}$. 5. Next, simplify $\sqrt{18}$. Since $18 = 9 \times 2$, we have $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$. 6. Therefore, $\sqrt{-18} = i \times 3\sqrt{2} = 3i\sqrt{2}$. 7. The simplest radical form of $\sqrt{-18}$ is $3i\sqrt{2}$.