Question

write the radical as a pure imaginary number.\\(sqrt{-294}\\)\\(sqrt{-294} = square\\)(simplify your answer. type an exact answer, using radicals as needed. express con

Explanation:

Step1: Rewrite the radical

We know that $\sqrt{-a}=\sqrt{a}\cdot\sqrt{-1}$ for $a\geq0$, and $\sqrt{-1}=i$. So we can rewrite $\sqrt{-294}$ as $\sqrt{294}\cdot\sqrt{-1}$.

Step2: Simplify $\sqrt{294}$

Factor 294: $294 = 49\times6$, and $\sqrt{49\times6}=\sqrt{49}\times\sqrt{6}=7\sqrt{6}$ (since $\sqrt{49} = 7$).

Step3: Combine with the imaginary unit

Since $\sqrt{-1}=i$, we have $\sqrt{-294}=\sqrt{294}\cdot i = 7\sqrt{6}i$.

Answer:

$7\sqrt{6}i$