Having problems with sq. root - √x - 4²√x - 5 = 0?

Question

I hope this makes sense - √x - 4²√x - 5 = 0

**Replace the small ² with 4. (Couldn't find shortcut on keyboard).

So the root is actually quad, not square.

I'm having problems getting rid of the quad. Would you also please explain how you get your answer. 10 pts. to clearest explanation. Thank you so much!

(sorry this is pre-cal review and I'm sucking at it...)

Answer 1

Note that you can write this as a quadratic equation in the fourth root of x; that is, because the fourth root of x squared is the square root of x, you can factor this as:

(x^(1/4) - 5)(x^(1/4) + 1)

Once you know the roots, you can solve for the fourth roots of x, which gives you a limited number of choices for x.  Plug those in and you're done.

Since you say you're doing a review, I'll leave that part for you.  Best of luck!