# How do you simplify 5sqrt(-75 )+ 3sqrt(-48)?

Jan 18, 2016

$37 \sqrt{3} i$

#### Explanation:

Consider the factors of (- 75 ) and )- 48 )

factors of ( - 75 ) = 25 $\times 3 \times \left(- 1\right)$

factors of ( - 48 ) = 16 $\times 3 \times \left(- 1\right)$

$\Rightarrow 5 \sqrt{-} 75 = 5 \sqrt{25} \sqrt{3} \sqrt{-} 1 = 5. 5 . \sqrt{3} . i = 25 \sqrt{3} i$

and $3 \sqrt{-} 48 = 3 \sqrt{16} \sqrt{3} \sqrt{-} 1 = 3 . 4 . \sqrt{3} . i = 12 \sqrt{3} i$

$\Rightarrow 5 \sqrt{-} 75 + 3 \sqrt{-} 48 = 25 \sqrt{3} i + 12 \sqrt{3} i = 37 \sqrt{3} i$