## karinewoods17 3 years ago combine {sqrt -8} + {sqrt -32}

1. karinewoods17

The answer in my book is $6i - 2i \sqrt{10}$ I dont know how they got that answer.

2. ilikephysics2

You can't take the square root of a negative number

3. ChmE

@ksaimouli is incorrect

4. karinewoods17

thats why you multiply it by i which is equal to -1

5. Ahaanomegas

@ksaimouli That's totally wrong. sqrt(a)+sqrt(b) is NOT sqrt(a+b). @ilikephysics2 Yes, You can. That's what imaginary numbers are there for. @karinewoods17 Notice that $\Large {\sqrt {8} = 2\sqrt{2}}$and $\Large {\sqrt {32} = 4\sqrt{2}},$so $\Large {\sqrt {-8} = 2i\sqrt{2}}$and $\Large {\sqrt {-32} = 4i\sqrt{2}}$Do you see how that works? Now, just add to get 6isqrt(2).

6. karinewoods17

wouldnt it be $6i \sqrt{2}$ ??

7. ChmE

$\sqrt{-8}+\sqrt{-32}=\sqrt{-8}+\sqrt{-8\times4}= \sqrt{-8} + 2\sqrt{-8}$

8. ChmE

$3\sqrt{-8}=3i \sqrt{8}=3i \sqrt{2\times4}=6i \sqrt{2}$

9. ChmE

Yes you are correct

10. Ahaanomegas

Yep. That's exactly what I said, except I explained everything. =P

11. karinewoods17

but... the answer in my book says the answer is $6i - 2i \sqrt{10}$ How did they get that?

12. karinewoods17

Im sorry:/ Im making coffee and waiting for you:)

13. karinewoods17

im not! sorry!

14. karinewoods17

I was making breakfast for my boyfriend.

15. karinewoods17

umm. $\sqrt{-32}$ breaks into $\sqrt{-32} = \sqrt{4} * \sqrt{-8}$ which simplifies to $4i \sqrt{2}$ ?

16. karinewoods17

And yes I try:)

17. karinewoods17

now what. lol

18. karinewoods17

@nincompoop please do not ignore me;)