Algebra help with roots

June 10, 2009 4:32 AM

I need help with a math problem my sister-in-law has for homework. It involves adding and multiplying roots and it's been long enough since college that I don't quite remember how to do that. The question is: 3sq(5)[2sq(5)-5]. I did it two different ways, getting 15sq(5) once and 9sq(5) the next. Is either right? An answer would be appreciated and, moreover, an explanation as to how to do it. Thanks!
posted by dbooster to Education (7 answers total)

Assuming sq(5) means the square root of 5:

3sq(5) [ 2sq(5) - 5 ] =

3sq(5)*2sq(5) - 5*3sq(5) =

6*sq(5)*sq(5) - 15sq(5) =

6 * 5 - 15sq(5) =

30 - 15sq(5) =

15 [ 2 - sq(5) ]
posted by Blazecock Pileon at 4:40 AM on June 10, 2009 [2 favorites]

Response by poster: Thank you kindly, sir. I am with you until the second to last step. When I did it, I made it that far and then subtracted the 15 from 30, which is how I came to my answer of 15sq(5). I can't quite follow how you made the leap from 30-15sq(5) to the answer, tho.
posted by dbooster at 5:14 AM on June 10, 2009

For the last step, try replacing sq(5) with x, so you can see it more clearly.

30 - 15x =
15 [2 - x] =
15 [2 - sq(5)]

You're dividing out a common factor. You cannot subtract the 15 from 30 because there's no independent 15.
posted by jeather at 5:24 AM on June 10, 2009

Response by poster: ahh I see now. Thank you, both of you.

(I guess this is practice for when I have kids and have to help with their hw...)
posted by dbooster at 5:48 AM on June 10, 2009

Just as an FYI, you can actually use google to do math -- including square roots.

3sqr(5) X ((2sqr(5))-5)

However, it gives you actual number answers, so not as useful here where you need the squareroots in the answer. Nevertheless, good way to check your work.
posted by davidnc at 7:07 AM on June 10, 2009

Wolfram Alpha wins!
posted by dmd at 7:37 AM on June 10, 2009 [3 favorites]

Wolfram alpha can also be used to check work, e.g.
posted by qxntpqbbbqxl at 7:41 AM on June 10, 2009 [2 favorites]