Question

How do I multiply the sqaure roots of two negative numbers?

Answer 1

Give an example. You would understand better with an example. -1=i

Answer 2

\[\sqrt{-a} \times \sqrt{-b} = \sqrt{ab}\]

Answer 3

\[\sqrt{-7}\sqrt{-168}\]

Answer 4

\[\sqrt{-7} \sqrt{-168} = \sqrt{7 \times 168} = \sqrt{1176} \approx 34.29\]

Answer 5

Thanks for the help! Are you certain this is correct? and how do you find the square roots of such large numbers?

Answer 6

Hmm. If you're supposed to leave it in radical form:
\[\sqrt{-7}\sqrt{-168} = \sqrt{-7}\sqrt{-7\times24} = 7\sqrt{24} = 14\sqrt{6}\]

Answer 7

I think you should look again at your answer, hicninja

Answer 8

I suppose you could factor out "i" from each of the square roots and get the negative of my answer as the answer, but actually both are correct.

Answer 9

\[\sqrt{-a}\sqrt{-b}=\sqrt{-1a}\sqrt{-1b}=i \sqrt{a} i \sqrt{b}= i ^{2}\sqrt{a} \sqrt{b} =-\sqrt{a} \sqrt{b}\]

Answer 10

Either is correct. When factoring \[\sqrt{-1}\] out of a negative radical, you get \[\pm i\]. See here: http://mathforum.org/library/drmath/view/53873.html

Answer 11

-i -i = i^2 = -1

Answer 12

but you factored out 2 i's. So you have:
\[\pm i \times \pm i = \pm 1\]

Answer 13

because the first i could be positive, and the second negative, or vice-versa.

Answer 14

You need to be consistent, either factor out 2 negative i's or 2 positive i's ie -1.

Anyway, http://www.wolframalpha.com/input/?i=sqrt%28-7%29sqrt%28-168%29

Answer 15

You don't need to be consistent. However, Google also gives your answer. I maintain either answer is accurate. :-)

Answer 16

look, just go to http://en.wikipedia.org/wiki/Imaginary_unit and scroll down to the section "proper use"

Of course, you can maintain your position if you wish, but it will cost you marks:-)

Answer 17

OK, you win. At least the last sentence implies the problem should be specified as:
\[i\sqrt{a}\times i\sqrt{b}\]
so as to avoid this kind of confusion. :-)

Answer 18

As I was careful to do in my derivation.

if you are asking me whether i is a bit flaky sometimes, well I would agree with you.

Sometimes the definitions get mixed up with the conventions.

Answer 19

Come on hickninja, don't give in so easily: fight.