Question

Solve the radical equations. Check for extraneous solutions.

Answer 1

\[2(x+1)^{2/3}-8=0\]

Answer 2

ok so we first get all the stuff in the parenthesis by itself to one side

Answer 3

Add 8?

Answer 4

exactly :)

Answer 5

May take me a moment to reply, gonna write it down as we go.

Answer 6

I understand, no problem ^_^

Answer 7

\[2(x+1)^{2/3}=8\]

Answer 8

good good :)

Answer 9

Wouldn’t I distribute the 2 to the \[x+1\]

Answer 10

hmm maybe if there wasn't an exponent, but you can't with the exponent there

for example:
2(x)^2 = 2 x^2
but
(2x)^2 = (2x)*(2x) = 4 x^2
which is not the same

you can't distribute the 2 when the exponent is on the outside of those parenthesis

instead, we can try to divide 2 from both sides

Answer 11

\[(x+1)^{2/3}=4\]

Answer 12

And then raise each side by \[^{3/2}\] to cancel out the \[^{2/3}\]?

Answer 13

that's correct :)
you got this :thumbs-up:

Answer 14

(x+1)=8

Answer 15

perfect

Answer 16

Subtract 1?

Answer 17

mhm

Answer 18

YAY!

Answer 19

Posting another