Please Help! What is the sum of √ -2 and √ -18?

[tex]\bf \sqrt{-2}+\sqrt{-18} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{-2}\implies \sqrt{-1\cdot 2}\implies \sqrt{-1}\cdot \sqrt{2}\implies \boxed{i\sqrt{2}} \\\\\\ \sqrt{-18}\implies \sqrt{-1\cdot 18}\implies \sqrt{-1}\cdot \sqrt{18}\implies i\sqrt{9\cdot 2}\implies i\sqrt{3^2\cdot 2}\implies \boxed{3i\sqrt{2}} \\\\[-0.35em] ~\dotfill\\\\ i\sqrt{2}+3i\sqrt{2}\implies 4i\sqrt{2}\implies \blacktriangleright 4\sqrt{2}~i \blacktriangleleft[/tex]

carlosego carlosego · Answer 2 · 2019-02-05T01:33:20+01:00

Answer:

Option 2. : [tex]4\sqrt{2}i[/tex]

Step-by-step explanation:

We must use the properties of roots and complex numbers.

We know that:

[tex]\sqrt{-1} = i[/tex]

Then we can write [tex]\sqrt{-18}[/tex] as:

[tex]\sqrt{9(2)(-1)}\\\\3\sqrt{2(-1)}\\\\3\sqrt{2}(\sqrt{-1})\\\\3\sqrt{2}i[/tex]

Something similar can be done with [tex]\sqrt{-2}[/tex]

[tex]\sqrt{-2} = \sqrt{2(-1)}\\\\\sqrt{2}i.[/tex]

Finally the sum of both terms is:

[tex]\sqrt{2}i. + 3\sqrt{2}i = 4\sqrt{2}i[/tex]