Question

What’s the answer to this ?

Answer 1

Option B:

Sum of $\sqrt{-2}$ and $\sqrt{-18}$ is $4\sqrt{2}i$.

Solution:

Given data:

$\sqrt{-2}$ and $\sqrt{-18}$

To find the sum of $\sqrt{-2}$ and $\sqrt{-18}$.

Sum of $\sqrt{-2}$ and $\sqrt{-18}$

                   $=\sqrt{-2} +\sqrt{-18}$

                   $=\sqrt{-2} +\sqrt{-2\times 9}$

                   $=\sqrt{-2} +\sqrt{-2\times 3^2}$

                  $=\sqrt{-2} +3\sqrt{-2}$

                  $=\sqrt{-1\times 2} +3\sqrt{-1\times2}$

The value of $\sqrt{-1} =i$.

                  $=\sqrt{2}i +3\sqrt{2}i$

                  $=4\sqrt{2}i$   (add the coefficient of √2i, i.e. (3 + 1 = 4))

Sum of $\sqrt{-2}$ and $\sqrt{-18}$ is $4\sqrt{2}i$.

Option B is the correct answer.