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

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

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  1. [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]

  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!

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