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Help! Denesting nested radicals.

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Help! Denesting nested radicals. [#permalink] New post 01 Dec 2012, 13:41
Can anyone explain how to solve a problem like this one?
sqrt(y+(sqrt(y+(sqrt(y)))))=2

What is the value of y? That's the entire problem.

Last edited by A777 on 02 Dec 2012, 08:49, edited 3 times in total.
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Re: Help! Denesting nested radicals. [#permalink] New post 01 Dec 2012, 23:55
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Re: Help! Denesting nested radicals. [#permalink] New post 02 Dec 2012, 13:06
Square both sides. Keep doing this until there are no square roots.
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Re: Help! Denesting nested radicals. [#permalink] New post 04 Dec 2012, 06:50
The equation can be rewritten as 2 = Sqrt(y + sqrt(y +.....))
So square both sides:
4 = (y + sqrt(y +.....))

So if 4 = (y + sqrt(y +.....)) and the original equation has an infinite number of (y + sqrt(y +.....)) terms, then you can substitute x^2 in the original equation.

I.e.
2 = Sqrt(y + sqrt(y +.....))
2 = Sqrt(y + 4)
+/-2 = y + 4

So y = 2-4 = -2
Or y = -2-4 = -6
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Re: Help! Denesting nested radicals. [#permalink] New post 04 Dec 2012, 06:50
The equation can be rewritten as 2 = Sqrt(y + sqrt(y +.....))
So square both sides:
4 = (y + sqrt(y +.....))

So if 4 = (y + sqrt(y +.....)) and the original equation has an infinite number of (y + sqrt(y +.....)) terms, then you can substitute x^2 in the original equation.

I.e.
2 = Sqrt(y + sqrt(y +.....))
2 = Sqrt(y + 4)
+/-2 = y + 4

So y = 2-4 = -2
Or y = -2-4 = -6
_________________

In the study cave!

Re: Help! Denesting nested radicals.   [#permalink] 04 Dec 2012, 06:50
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Help! Denesting nested radicals.

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