Question 7 Simplify. \( \sqrt{-63} \)

To simplify \( \sqrt{-63} \), we start by factoring out the negative sign. We can express it as \( \sqrt{-1 \cdot 63} \). Here, \( \sqrt{-1} \) is represented by the imaginary unit \( i \), which leads us to \( i\sqrt{63} \). Now, \( \sqrt{63} \) can be further simplified since it equals \( \sqrt{9 \cdot 7} = 3\sqrt{7} \). So, we finally get \( \sqrt{-63} = 3i\sqrt{7} \). For a quick recap, whenever you encounter a square root of a negative number, think of \( i \) as your faithful guide to the imaginary realm. This handy tip can transform seemingly tricky problems into manageable ones! Just remember, it’s like popping into an alternate universe where every negative square root is a new adventure waiting to be simplified!