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

Dec 13, 2016

${8}^{\sqrt{6}} \approx 162.971$

#### Explanation:

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:

${8}^{\sqrt{6}} = {e}^{\sqrt{6} \cdot \ln \left(8\right)} \approx 162.97074840462838867617$

Truncated to $3$ decimal places this would be:

$162.970$

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

${8}^{\sqrt{6}} \approx 162.971$