Question

Can I get some help simplifying a few problems? Such as 1) sqrt 108x^3y^2

Answer 1

So, with this you can only pull out the constant, because the variables can be values that would make splitting them erroneous.
\[\sqrt{108x^3y^2}=\sqrt{108}\sqrt{x^3y^2}\]
try simplifying that

Answer 2

Alright, one moment.

Answer 3

btw, if we know that x,y are positive, we could split it a bit more. if they do become negative the imaginary parts are what keep us from splitting them

Answer 4

I do know that with a square root, by the way I was taught would lead to x^3 to being something like this: \[xy \sqrt{108x}\]

Answer 5

right, it is correct to lead polys with the highest exponents first. in this case, we just pull the constant out and simplify that, since that's all we can really do

Answer 6

So, would that be this? : \[6xy \sqrt{3x}\]

Answer 7

right, \[xy(108x)^{\frac12}=6xy(3x^{\frac12})\]

Answer 8

OH, got it.

Answer 9

oh, sorry, i just default to doing that--i havent written a sqrt sign in years..
\[\sqrt{x}=x^{\frac12}\]

Answer 10

1/2 is just simply saying 'The square root.'

Answer 11

Um, would you mind helping me with my other problems?

Answer 12

right, and cubed root is 1/3 fourth root is 1/4

Answer 13

sure.

Answer 14

The next one up is \[\sqrt{-162}\]

Answer 15

so the negative just tells us there will be an i in front. so whats \(\sqrt{162}\) ? then just put an i in front

Answer 16

So, \[9\sqrt{2i}\]?