Math Olympiad Australia Problem

In this blog we are going to solve this math olympiad problem from Australia

 Solution
`\sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}`

Let the above equation be say x , we get

`x=  \sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}`

Now do square on Both sides we will get 

`x^{2}=  7\sqrt{7\sqrt{7\sqrt{7...}}}`

put `x=  \sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}` in the above equation we get
`x^{2} = 7x`


Cancelling x on both sides we get

`x =7`
and that is the answer