Question

express the radical using the imaginary unit, ( i ). express your answer in simplified form. ( pmsqrt{-24}=pm )

Explanation:

Step1: Rewrite the radical

We know that $\sqrt{-a}=\sqrt{a}\cdot\sqrt{-1}$ for $a\geq0$. So, $\pm\sqrt{-24}=\pm\sqrt{24}\cdot\sqrt{-1}$.

Step2: Simplify $\sqrt{24}$

Factor 24: $24 = 4\times6$. Then $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}$.

Step3: Substitute $\sqrt{-1}$ with $i$

Since $\sqrt{-1}=i$, we have $\pm\sqrt{24}\cdot\sqrt{-1}=\pm2\sqrt{6}\cdot i=\pm2i\sqrt{6}$.

Answer:

$\pm 2i\sqrt{6}$