Option B:
Sum of [tex]\sqrt{-2}[/tex] and [tex]\sqrt{-18}[/tex] is [tex]4\sqrt{2}i[/tex].
Solution:
Given data:
[tex]\sqrt{-2}[/tex] and [tex]\sqrt{-18}[/tex]
To find the sum of [tex]\sqrt{-2}[/tex] and [tex]\sqrt{-18}[/tex].
Sum of [tex]\sqrt{-2}[/tex] and [tex]\sqrt{-18}[/tex]
[tex]=\sqrt{-2} +\sqrt{-18}[/tex]
[tex]=\sqrt{-2} +\sqrt{-2\times 9}[/tex]
[tex]=\sqrt{-2} +\sqrt{-2\times 3^2}[/tex]
[tex]=\sqrt{-2} +3\sqrt{-2}[/tex]
[tex]=\sqrt{-1\times 2} +3\sqrt{-1\times2}[/tex]
The value of [tex]\sqrt{-1} =i[/tex].
[tex]=\sqrt{2}i +3\sqrt{2}i[/tex]
[tex]=4\sqrt{2}i[/tex] (add the coefficient of √2i, i.e. (3 + 1 = 4))
Sum of [tex]\sqrt{-2}[/tex] and [tex]\sqrt{-18}[/tex] is [tex]4\sqrt{2}i[/tex].
Option B is the correct answer.
