Can somebody explain how my solutions manual went from (- 2 + √-20)/6 to - 2/6 + (2i√5)/6? I don't see how they came up with the 2i*5^2=-20^2. i = -1^2. Equation editor is not working for me..

Question

Can somebody explain how my solutions manual went from (- 2 + √-20)/6 to - 2/6 + (2i√5)/6? I don't see how they came up with the 2i*5^2=-20^2. i = -1^2.  Equation editor is not working for me..

anonymous · Answer

The square root of -1 is i.

sqrt(-20) = sqrt(-1 * 4 * 5)

Take out the -1 and the 4 and you get 2i * sqrt(5)

anonymous · Answer

$$\sqrt{-20} = \sqrt{-1\times 4\times 5} $$$$= \sqrt{-1}\times \sqrt{4} \times \sqrt{5}$$$$=i \times 2 \times \sqrt{5}$$$$=2i\sqrt{5}$$

anonymous · Answer

2i*sqrt(5) would equal -10, would'nt it?

anonymous · Answer

No.  It equals $$2i \sqrt{5}$$

anonymous · Answer

I'm, confused...

anonymous · Answer

When you have the square root of a negative number, you need to break it up like polpak did.  You can factor out the square root of -1 which is always equal to i.

anonymous · Answer

It would also equal $2\sqrt{-5}$ or $i\sqrt{20}$

anonymous · Answer

But the simplest form is the one I gave you originally.