Perform Operations with Square Roots of Negative Numbers
Perform the indicated operations and write the result in standard form.
-$2 \sqrt { - 45 } + 5 \sqrt { - 20 }$
A) $16 \mathrm { i } \sqrt { 5 }$
B) $- 16 \sqrt { 5 }$
C) $16 \sqrt { 5 }$
D) $- 16 \mathrm { i } \sqrt { 5 }$

Question

Quizplus · Accepted Answer

First, simplify each term: $2\sqrt{-45} = 2\sqrt{9 \cdot 5 \cdot -1} = 2 \cdot 3\sqrt{5}i = 6\sqrt{5}i$ and $5\sqrt{-20} = 5\sqrt{4 \cdot 5 \cdot -1} = 5 \cdot 2\sqrt{5}i = 10\sqrt{5}i$. Adding these gives $6\sqrt{5}i + 10\sqrt{5}i = 16\sqrt{5}i$.

Perform Operations with Square Roots of Negative Numbers Perform the Indicated

Perform Operations with Square Roots of Negative Numbers
Perform the Indicated