Question

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

Answer 1

`\bf √(-2)+√(-18) \\\\[-0.35em] ~\dotfill\\\\ √(-2)\implies √(-1\cdot 2)\implies √(-1)\cdot √(2)\implies \boxed{i√(2)} \\\\\\ √(-18)\implies √(-1\cdot 18)\implies √(-1)\cdot √(18)\implies i√(9\cdot 2)\implies i√(3^2\cdot 2)\implies \boxed{3i√(2)} \\\\[-0.35em] ~\dotfill\\\\ i√(2)+3i√(2)\implies 4i√(2)\implies \blacktriangleright 4√(2)~i \blacktriangleleft`

Answer 2

Option 2. :
`4√(2)i`

Explanation:

We must use the properties of roots and complex numbers.

We know that:

`√(-1) = i`

Then we can write
`√(-18)` as:

`√(9(2)(-1))\\\\3√(2(-1))\\\\3√(2)(√(-1))\\\\3√(2)i`

Something similar can be done with
`√(-2)`

`√(-2) = √(2(-1))\\\\√(2)i.`

Finally the sum of both terms is:

`√(2)i. + 3√(2)i = 4√(2)i`