Help with Radical question please

G

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Guest
Solve the equation:


4____ 4 ______
\/x+6 = \/ 2x-8


Have no idea how to start.
 
Haven't you already posted this elsewhere? And received two solutions? If this is different, then please reply with clarification: What are the 4's? Are they indices, and these are fourth roots? Or are they numerators, and the denominators are square roots?

Eliz.
 
Maybe

I didn't check totally yet. The question consisted of

sqrt of x+6 to the 4th root = sqrt of 2x-8 to the 4th root.

The other site said to cancel the 4's...why??? then square both sides.

x+6=2x-8 and square these. Do you agree?
 
Is it a square root to a fourth power? Or a fourth root? Or the square root of a fourth root? These are very different things, whose notation and terminology should have been mentioned in class. Without knowing what we're dealing with, it is difficult to know how to proceed.

Eliz.
 
thanks

The 4th root.

4rth sqrt of x+6 = 4th sqrt of 2x-8.

I don't know how to do the square root symbol on the keyboard. Did this help? Sorry for not being able to be clear.
 
The square root is the second root. The fourth root is the fourth root. There is no "fourth square root". (Your book and instructor aren't teaching you the notation and terminology solely to be annoying. If you don't know the lingo, you can't communicate with others, and this makes it very difficult for those others to help you. You are asking volunteers to give of their time; please have the courtesy to speak clearly. Thank you.)

I will guess (since grouping symbols are still not being used) that everything on either side of the equation is supposed to be included inside the radicals, so we have:

. . . . .4th-rt(x + 6) = 4th-rt(2x - 8)

Raise both sides to the fourth power to cancel the radicals (since a fourth power is the inverse of a fourth root), and solve the resulting linear equation:

. . . . .x + 6 = 2x - 8

(The process and answer will, of course, be quite different if my initial assumption was incorrect.)

Eliz.
 
thank you

I will get it from here. Yes, my book and teacher are very vague on so much. I am only taking this class to update myself to help my kids, but maybe that is why it is harder for me to understand the language??? I will go from here, but I want to thank you for your time, and I will in the future try to do my best with the symbols and language.
 
.4th-rt(x + 6) = 4th-rt(2x - 8)

Raise both sides to the fourth power to cancel the radicals (since a fourth power is the inverse of a fourth root), and solve the resulting linear equation:

. . . . .x + 6 = 2x – 8

Hi, Amy,

Eliz. has given you most of the work, but one thing has not been mentioned. Whenever you are taking an even root (as in this case: 4), the expression inside/under the radical (the “square root symbol”, which is really for any root, not just square roots, as Eliz. explained) cannot be a negative number. If you solve for

x + 6 = 2x – 8, you get
x = 14, which is correct.

It is important that you always substitute your solution back into the original expressions to make sure they don’t give you a negative number inside the radical. 14 works just fine in this case.

Hope that helps.
 
thanks

I did come up with that! I thank you for your work too!
 
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