Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals. $sqrt{-96}$

Explanation:

Step1: Factor out -1 from radicand

$\sqrt{-96} = \sqrt{-1 \times 96}$

Step2: Separate the radicals

$\sqrt{-1 \times 96} = \sqrt{-1} \times \sqrt{96}$

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

$\sqrt{-1} \times \sqrt{96} = i\sqrt{96}$

Step4: Simplify $\sqrt{96}$

$\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}$

Step5: Combine terms

$i \times 4\sqrt{6} = 4i\sqrt{6}$

Answer:

$4i\sqrt{6}$