Question

What is the square root of 2 to the power of 1000?

Answer 1

`sqrt(2)^1000 = sqrt(2)^(2xx500) = (sqrt(2)^2)^500 = 2^500`

An approximate value for this would be `10^150` since `2^10 = 1024 ~= 1000 = 10^3`

For a little more accuracy, use `log_10 2 ~= 0.30103`

then `log_10 (2^500) = 500 log_10 2 ~= 500 xx 0.30103 = 150.515`

So `2^500 ~= 10^150.515`

Using an arbitrary precision calculator

`sqrt(2)^1000 = 2^500`

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