what is the sum of $sqrt{-2}$ and $sqrt{-18}$?\n$4sqrt{2}$\n$4isqrt{2}$\n$5sqrt{2}$\n$5isqrt{2}$
what is the sum of $sqrt{-2}$ and $sqrt{-18}$?\n$4sqrt{2}$\n$4isqrt{2}$\n$5sqrt{2}$\n$5isqrt{2}$
Answer
Explanation:
Step1: Simplify square - roots of negative numbers
Recall that $\sqrt{-a}=i\sqrt{a}$ for $a>0$. So, $\sqrt{-2}=i\sqrt{2}$ and $\sqrt{-18}=i\sqrt{18}$. Since $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$, then $\sqrt{-18}=i\times3\sqrt{2}=3i\sqrt{2}$.
Step2: Add the two complex - numbers
$\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=(1 + 3)i\sqrt{2}=4i\sqrt{2}$.
Answer:
$4i\sqrt{2}$ (corresponding to the second option)