anonymous 5 years ago Ok, I need help figuring out, (-7 + sqrt-5) ^2. I know it's re-written as (-7 + sqrt -5) (-7 + sqrt -5). Do I use FOIL to figure this out?

1. KingGeorge

FOIL would be an excellent strategy in this case.

2. anonymous

Yes, but rewrite it. sqrt -5 means imaginary..

3. anonymous

|dw:1327303757412:dw|

4. anonymous

how do I rewrite it? I think that's the part that's stumping me

5. anonymous

oh wait, Cinar already did. Thanks! so sqrt -5 equals sq root 5i?

6. KingGeorge

The equation you have is the following correct?$(-7 + \sqrt{-5})^2$

7. anonymous

|dw:1327303914040:dw|

8. anonymous

@kinggeorge: Yes, that is correct! how did you get the square root symbo??

9. KingGeorge

If you go into the equation editor on the bottom left of the comment box. For example, you can type "sqrt{-5}" without the quotes to get $\sqrt{-5}$It takes some getting used to, but is very clear. Moving on, since that is the equation, cinar's solution is correct.

10. anonymous

I know it's the imaginary units that are throwing me off

11. KingGeorge

As for imaginary units, the square root of negative one is defined as the letter i. Or, $\begin{matrix} \sqrt{-1} = i \\ i^2 = -1 \end{matrix}$So if you have a radical such as $\sqrt{-20}$ you can simplify and solve like so$\sqrt{-20} = \sqrt{(-1) \cdot 4 \cdot 5} = \sqrt{-1} \cdot \sqrt{4} \cdot \sqrt{5} = 2i \sqrt{5}$

12. anonymous

wow, this is great!! thank you so much. It's making a lot more sense to me now!

13. KingGeorge

you're very welcome