Determine the exact value of (Square Root of Square Root)

[n3w ton]

Determine the exact value of... (Square Root of Square Root)

I was looking through my textbook and saw a interesting question, I attempted but couldn't get it. (The Answer in Back of Text Book Was Different From Mine..)

Question
Determine the exact value of...

√10+√10+√10...


I tried typing it as well as I can , I uploaded image of question just in case :D

Determine the exact value of:

 

[micromass]

Let

$$x=\sqrt{10+\sqrt{10+\sqrt{10+...}}}$$

What is

$$x^2-10$$

Does this give you an equation that you can solve??