# Continued root of 2

#### DrizzlyDays

Hey guys,

I'm having trouble with this question here.

I have to find the value of the continued root of 2 (shown in image) algebraically. Could someone please walk me through it?

p.s. the question gives a hint saying "Find X^2 in terms of X"

Thanks ^_^

#### undefined

MHF Hall of Honor
Hey guys,

I'm having trouble with this question here.

View attachment 18036

I have to find the value of the continued root of 2 (shown in image) algebraically. Could someone please walk me through it?

p.s. the question gives a hint saying "Find X^2 in terms of X"

Thanks ^_^
First note that X can't be negative, because of the definition of $$\displaystyle \sqrt{}$$. Then square both sides. What do you see?

DrizzlyDays

#### DrizzlyDays

Well, wouldn't it be:

X^2 = 2 + *continued root*?

or does squaring it get rid of more than just one surd?

#### DrizzlyDays

OH WAIT i see it now....

X^2 = 2 + X
X^2 - X - 2 = 0
(X-2)(X+1) = 0

so X = 2 or X = -1

so it must equal 2 because it can't be negative

=D thanks