A useful math hack…

How to easily solve a nested radical equation,,,

math hack nested radicals

You can adapt it to any repeating basic math operator in the infinitely nested radicals. The above nested radicals can be equal to whatever you want except 1, this is due to the particular multiplicative identity properties of the digit 1 (for instance, √1 = 1 and 1² = 1).

To resume, the solution to these expressions is always:
x = N² – N for N > 0 and N ≠ 1   (N = any number)

Square root of zero?

Though the square root of zero is obviously zero, the limit of the following nested radicals equals 1 when n approaches 0. Strange, isn’t it?

math hack nested radicals 2