Question

How to multiply radicals? Wait a moment while I type out some examples...

Answer 1

\[2+\sqrt{2} (\times) 2+\sqrt{2}\]\[3+\sqrt{2}(\times)2+\sqrt{5}\]

Answer 2

\[3+\sqrt{2}(\times)2+\sqrt{8}\]\[\sqrt{2}+\sqrt[3]{2}(\times)\sqrt{6}+\sqrt[3]{4}\]

Answer 3

For the first example, do you mean this? \[(2+\sqrt{2})*(2+\sqrt{2})\]

Answer 4

Yeah, that's what I meant for all of them. Thank you. :)

Answer 5

No problem :) For future reference, the LaTeX you're looking for was this: (2+sqrt{2})*(2+sqrt{2}). Before we work on the examples, can you tell me what (a+b)(a+b) is?

Answer 6

Ah, I see, cool. :)
Uh, I'm not entirely sure? I've taken these from shapes that I have to find the area of. I made these equations from the given questions.

Answer 7

Okay, I'll just tell you then: \[(a+b)(a+b)=a(a+b)+b(a+b)=a^2+ab+ba+b^2=a^2+ 2ab + b^2\]Do you understand this so far?

Answer 8

I think so...I'm supposed to keep them in radical form as well. So I don't have to solve it necessarily.

Answer 9

Don't worry, they will be :) So we know \[(a+b)(a+b)=a^2+2ab+b^2 \]
Our first question was \[(2+\sqrt{2})*(2+\sqrt{2})\]If we let a=2 and b=sqrt(2), then put it into the first equation we have, can you tell me what we get out of it?

Answer 10

In general, when you have something like:\[
\sqrt{2}\times 2
\]The simplified form would be:\[
2\sqrt 2
\]

Answer 11

If we have something like:\[
\sqrt{2}\times \sqrt{6}
\]Then we can multiply what is in the radicals:\[
\sqrt{2\times 6} =\sqrt{12}
\]However, typically we want to factor our numbers into primes:\[
\sqrt{2}\times\sqrt{2}\times\sqrt{3}= 2\times \sqrt 3=2\sqrt 3
\]