Rewrite this imaginary number using i and then select your answer from the choices. Make sure your answer is fully simplified. \[ \sqrt{-25} \]
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The expression \(\sqrt{-25}\) can be rewritten using the imaginary unit \(i\) as follows: \(\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i\). So, the fully simplified answer is \(5i\). Now let's have some fun facts! First Line: Imaginary numbers, like \(i\), were first introduced by the Italian mathematician Gerolamo Cardano in the 16th century. He encountered them while attempting to solve cubic equations, which set the stage for many sophisticated developments in mathematics! Second Line: Imaginary numbers aren't just abstract concepts; they play crucial roles in electrical engineering and quantum physics! For instance, in circuit analysis, engineers use complex numbers to analyze waveforms, making sense of alternating current (AC) systems in a delightful way!
