MATH

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I don't understand how to visualize 3^[2^(1/2)].

Please tell me how you visualize it.

^^ Greetings Noxide. I believe you may visualise the happy friend using the exponential function. Here we are considering 3 to the square root of 2. This is also equal to exp((2^1/2)ln(3)) where exp of some number is often represented as e to some number. exp(x) is defined as the limit as n tends to infinity of (1+x/n)^n (I am sorry if this is incorrect of me). So in this case, your original number that you posted should be the limit as n tends to infinity of (1+((2^1/2)ln(3))/n)^n.

^^ I do hope that is of help for you. If you do need any more explanation, I would be very to attempt to explain a litt.e more. I am very sorry as I am not very skilled at explaining.

I would visualize it as an approximation. Even though the square root of 2 is irrational, it is a value. I visualize it as the length of the hypotenuse of a right triangle with sides = 1. The value is a little over 1.414.

3^1.414 = 4.728 (rounded to 3 decimal places). The actual answer is 4.728804388.