Perform the operation and write the result in standard form. $\sqrt { - 28 } + \sqrt { - 112 }$
A) $9 i \sqrt { 7 }$
B) $\sqrt { 11 } i \sqrt { 7 }$
C) $- 5 i \sqrt { 7 }$
D) $6 i \sqrt { 7 }$
E) $- 2 i \sqrt { 7 }$

Question

Quizplus · Accepted Answer

We can first simplify both square roots by factoring out the greatest perfect square factor from each of them:

$$\sqrt{-28}+\sqrt{-112}=\sqrt{-4\cdot7}+\sqrt{-16\cdot7}=2i\sqrt{7}+4i\sqrt{7}=6i\sqrt{7}$$

Therefore, the answer is choice D.

Perform the Operation and Write the Result in Standard Form −28+−112\sqrt { - 28 } + \sqrt { - 112 }−28​+−112​

Perform the Operation and Write the Result in Standard Form $\sqrt { - 28 } + \sqrt { - 112 }$