Question

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

Answer 1

Answer:

$\large\boxed{\sqrt{-2}+\sqrt{-18}=4\sqrt2\ i}$

Step-by-step explanation:

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

Answer 2

The sum of √-2 and √-18 is 4√2i.

What is the square root of -1?

The square root of -1 is an imaginary number which is represented by i.

√-1=i

Here we have to calculate √-2+√-18

√-2+√-18

=√(-1).2+√(-1).18

=√(-1).√2+√(-1).√18

=i√2+i√18             (as √-1=i where i is imaginary number)

But √18=√(9*2)=√9*√2=3√2    

(as √(ab)=√a.√b)

=i√2+i3√2

=√2(i+3i)

=√2*4i

=4√2i

Therefore the sum of √-2 and √-18 is 4√2i.  

Learn more about imaginary number

here: https://brainly.com/question/5564133

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