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

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