Question

Write in simplified radical form with at most one radical

sqrt cd^5 / ^6sqrt cd^2

Assume that all variables represent positive real numbers.

Answer 1

\[\Large\rm \frac{\sqrt{cd^5}}{\sqrt[6]{cd^2}}\]Is this what the problem looks like?

Answer 2

Yes @zepdrix

Answer 3

hmm

Answer 4

So what's the best approach here... hmm
Do you know how to write roots as rational expressions?
Example: \(\Large\rm \sqrt{x^3}=x^{3/2}\)
We might need to do that here.

Answer 5

\[\Large\rm \sqrt{cd^5}=c^{1/2}d^{5/2}\]Does that.. process.. look familiar or make sense? :d

Answer 6

Yes, but the thing is they want atleast one radical.
I got that answer though :)

Answer 7

`At most` one radical.
What'd you get for an answer? c:

Answer 8

Oh the top thing is your answer?

Answer 9

the same thing you got

Answer 10

It's quite a few steps away from having a single root.
Lemme show you :\

Answer 11

\[\Large\rm \frac{\sqrt{cd^5}}{\sqrt[6]{cd^2}}=\frac{(cd^5)^{1/2}}{(cd^2)^{1/6}}=\frac{c^{1/2}d^{5/2}}{c^{1/6}d^{2/6}}\]Then apply rules of exponents lets us divide the c's, and the d's, separately,\[\Large\rm c^{\left(\frac{1}{2}-\frac{1}{6}\right)}d^{\left(\frac{5}{2}-\frac{6}{2}\right)}=c^{1/3}d^{13/6}=c^{1/3}\left(d^{13/2}\right)^{1/3}\]And finally we can write them under a single root,\[\Large\rm \sqrt[3]{c d^{13/2}}\]Something like that... :(

Answer 12

These are so awful.

Answer 13

I mean I kind of understand.. it tests your knowledge of different exponent rules and radicals, but yah this seems kind of extreme...

Answer 14

For this level of work at least

Answer 15

I didn't explain all of the steps in there.
Lemme know if I should back up :U

Answer 16

Too much? did your head esplode?

Answer 17

yeah, I'm dying with these. No one in my class understands these. We had to skip the whole section. I'll just try my best hehe Thanks.

Answer 18

aw :3