# How do you express 3sqrt(-48) as a product of a real number and i?

May 21, 2018

$12 \sqrt{3} i$

#### Explanation:

$\text{using the "color(blue)"laws of radicals}$

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

$\sqrt{- 48} = \sqrt{16 \times 3 \times - 1}$

$\textcolor{w h i t e}{\times \times} = \sqrt{16} \times \sqrt{3} \times \sqrt{-} 1$

$\textcolor{w h i t e}{\times \times} = 4 \sqrt{3} i$

$\Rightarrow 3 \left(4 \sqrt{3} i\right) = 12 \sqrt{3} i$