need help finding 2 solutions for this equation.

Question

anonymous · Answer

$$y ^{2\over3}+5y ^{1\over3}-104=0$$

dumbcow · Answer

treat it just like a quadratic equation since (y^1/3)^2 = y^2/3
factor , what factors of -104 add up to 5

anonymous · Answer

i couldn't think of anything that does.

dumbcow · Answer

start with the obvious
52*2
then take half of 52 and double 2
26*4
13*8

anonymous · Answer

-13 and 8 work I guess

dumbcow · Answer

check the signs, they need to add up to positive 5

anonymous · Answer

13 and -8

dumbcow · Answer

ok so now
(y^1/3 +13)(y^1/3 - 8) = 0
solve each part for y

anonymous · Answer

so 13- 1/3 and 8-1/3?  Sorry, I know this is way more simple than I'm making it.

anonymous · Answer

i just don't know if it will end up not being a whole number this way? and what that would be exactly

dumbcow · Answer

thats ok
y^1/3 = -13
to get y by itself i have to take each side to the 3rd power
this way (y^1/3)^3 = y 
y = -13^3
also
y = 8^3

anonymous · Answer

oh ok. so the answers can be to the third power like that?

anonymous · Answer

my online assignment wont let me type the answer to the third power.  Do I solve more from there?

dumbcow · Answer

put it in your calculator to get a whole number

anonymous · Answer

one of them is 28561 and the other is4096..? kinda big numbers.

dumbcow · Answer

8^3 = 8*8*8 = 512
-13^3 = -13*-13*-13 = -2197

anonymous · Answer

ohho k, i didn't know the answers could be that large.

dumbcow · Answer

only because of the fractions in the exponents