What is $8^sqrt6$ rounded to three decimal places?

Question

2018 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-13T18:35:09

$8^sqrt(6) ~~ 162.971$

I can't think of a nice way of calculating this by hand, so let's resort to a calculator.

Assuming your calculator has $sqrt(x)$ key, $ln x$ key and $e^x$ key, we can calculate:

$8^sqrt(6) = e^(sqrt(6) * ln(8)) ~~ 162.97074840462838867617$

Truncated to $3$ decimal places this would be:

$162.970$

Note however, that the following digit is $7 >= 5$ , so we should round up the last digit from $0$ to $1$ to get:

$8^sqrt(6) ~~ 162.971$

What is 8^sqrt68^sqrt6 rounded to three decimal places?