Hello all, wondering if you could help me. I am brushing up on math to go back to school, and just looked over a practice test for algebra. The only question I couldn't figure out how to answer was this one:
[Sorry about the formatting. The whole fraction is under the radical here, in case this is ambiguous. I'm willing to make anything look neater if it's explained how.]
For all x>0 and y /=/ 0, which of the following expressions is equivalent to √x^4/ y^5 ?
> A) x^2 √y/y^3
> B) x^2 √y/y^3
> C) x^2/y^3
> D) x^2/ ³√y
> E) x^2 √y
I looked up the answer, and it still doesn't really make sense to me. Like, I know some basics about exponents. Like I think the square root of the exponent is the exponent times 1/2, which would give me x^2/y^(2.5), right? But I can't figure out how to relate that to these options, and clearly have some big gaps in my knowledge here. Any help would be appreciated.
(Again, sorry about the formatting. I know it's hard for me to read that)
OK, I feel like I am almost getting it, but in step 4, I'm not understanding how we got that √y in the numerator.
(Thanks for the help so far, btw. I really appreciate that a stranger on the internet took the time to do this.)
Edit: Oh, wait, I see, just multiplied both by √y? I'm not sure if I'm confused or not, lol.
Edit II: OK, now I got it. I sort of got it with edit I, but I just reconciled it with my statement that Wilmer confirmed, which made it click more somehow. I don't know what I'm talking about, but I get this answer now. Thanks.
Skittles, what was done by multiplying the numerator and denominator by SQRT(y)
is really a net multiplication by 1 : SQRT(y) / SQRT(y) = 1
This is a process known as "rationalizing the denominator": in other words, if there
is a SQRT(something) in denominator, get it out of there!
If you really want to see the why/how, go here:
OK, that makes even more sense then. My assumption was that it was just to because they didn't want a weird exponent (2 1/2), or else it was just sort of done to do it, and make you figure out which was the same.
I do remember this now, thank you.
(What is the end game for doing this? Like, I didn't get why we learned to factor >1st degree polynomials until I got to the problems where I needed it. Just sort of in general terms, when does it help up to have the radical in the numerator instead of the denominator?)
And thanks again for the help.