To determine the value of the expression [tex]\( 8 \sqrt{6} \)[/tex], follow these steps:
1. Identify the components: Recognize that the expression contains a constant (8) and a square root ([tex]\(\sqrt{6}\)[/tex]) which is the square root of 6.
2. Evaluate the square root: The square root of 6, which is approximately [tex]\(2.449\)[/tex]. This means [tex]\(\sqrt{6} \approx 2.449\)[/tex].
3. Multiply the constant by the square root: Multiply 8 by approximately [tex]\(2.449\)[/tex].
[tex]\[
8 \times 2.449 \approx 19.595
\][/tex]
4. Round to a reasonable number of decimal places if necessary: The precise value obtained is [tex]\(19.595917942265423\)[/tex].
Thus, the value of the expression [tex]\( 8 \sqrt{6} \)[/tex] is approximately [tex]\( 19.595917942265423 \)[/tex].
