Square root problem

x=√2+√2+√2+..... (all under 1 square root, so first √ is the main one, the next √ would be under the former √ , the third √ under the 2nd √ etc.)
√y+√y+√y+....=5

how would i solve for x or y, its somewhat confusing any help?

x = sqrt(2 + sqrt(2 + sqrt(2 + ....
Square both sides (you're going to love this)
x^2 = 2 + sqrt(2 + sqrt(2 + sqrt(2 + sqrt(2 + ....
x^2 = 2 + x
See how that happened? Just look at again and again until you see it. All I did was a quick substitution. Now we have a pretty simple quadratic formula to evaluate
x^2 - x - 2 = 0
(x - 2) * (x + 1) = 0
x = -1 , 2
sqrt(2 + sqrt(2 + sqrt(2 + ..... = -1 , 2
-1 is extraneous, so it equals 2


sqrt(y + sqrt(y + sqrt(y + ..... = 5
y + sqrt(y + sqrt(y + sqrt(y + .... = 25
y + 5 = 25
y = 25 - 5
y = 20

I love these kinds of problems.

x=√2+√2+√2+..... = sqrt(2 + x)

==> x^2 = 2 + x
==> x^2 - x - 2 = 0
x = -1,2

√y+√y+√y+....=5
==> sqrt(y+5) = 5 ==> y = 20