What is the sum of the square root of negative 2 and the square root of negative 18

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What is the sum of the square root of negative 2 and the square root of negative 18

[tex]\large\boxed{\sqrt{-2}+\sqrt{-18}=4\sqrt2\ i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\===================\\\\\sqrt{-2}+\sqrt{-18}=\sqrt{(2)(-1)}+\sqrt{(9)(2)(-1)}\\\\=\sqrt2\cdot\sqrt{-1}+\sqrt9\cdot\sqrt2\cdot\sqrt{-1}\\\\=\sqrt2\cdot i+3\cdot\sqrt2\cdot i\\\\=i\sqrt2+3i\sqrt2=4i\sqrt2[/tex]

ege

step-by-step explanation:

egge

1. i square root of 2

2. 3i square root of 2

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

=7

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

=3

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

=4

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!