Question

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Answer 1

Is the problem: \[\sqrt{x + \sqrt{2x}} = \sqrt{2x}\] ?

Answer 2

Yes. :)

Answer 3

If that's the case, then in the first line of your solution, where you squared both sides, the right side was not squared.

Answer 4

Square both sides:
x + sqrt(2x) = 2x
sqrt(2x) = x
square again:
2x = x^2
x^2 - 2x = 0
x(x-2) = 0
x = 0 or x = 2

Answer 5

Ahhh okay. I wasn't too sure. Thanks a lot!

Answer 6

You are welcome.

Answer 7

Since you squared both sides, you must check both solutions in the original equation to make sure they are not extraneous.

Answer 8

Good point @mathstudent55. I mentally checked both solutions but I should have included that in the reply.