For this case, we must add two negative roots:
[tex]\sqrt {-2} + \sqrt {-18}[/tex]
By definition, we know that:
[tex]i = \sqrt {-1}[/tex]
[tex]i^2=-1[/tex]
So:
[tex]\sqrt {-2} = \sqrt {2i ^ 2} = i \sqrt {2}\\\sqrt {-18} = \sqrt {18i ^ 2} = i \sqrt {18}[/tex]
Also:
[tex]\sqrt {18} = \sqrt {9 * 2} = \sqrt {2 * 3 ^ 2} = 3 \sqrt {2}[/tex]
So, we have:
[tex]i \sqrt {18} = 3i \sqrt {2}[/tex]
So, we have:
[tex]\sqrt {-2} + \sqrt {-18} = i \sqrt {2} + 3i \sqrt {2} = 4i \sqrt {2} = 4 \sqrt {2} i[/tex]
Answer:
Option b
