Let's break down the expression step by step to understand and compute it.
We need to determine the product of these terms:
[tex]\[ 2 \sqrt{8} \][/tex]
[tex]\[ \sqrt{8} \][/tex]
[tex]\[ 2 \sqrt{116} \][/tex]
First, we calculate each term individually.
1. Calculate [tex]\(2 \sqrt{8}\)[/tex]:
- The square root of 8 is [tex]\(\sqrt{8} \approx 2.8284271247461903\)[/tex].
- Multiplying this by 2:
[tex]\[
2 \sqrt{8} \approx 2 \times 2.8284271247461903 \approx 5.656854249492381
\][/tex]
2. Calculate [tex]\(\sqrt{8}\)[/tex]:
- As determined in the previous step, [tex]\(\sqrt{8} \approx 2.8284271247461903\)[/tex].
3. Calculate [tex]\( 2 \sqrt{116} \)[/tex]:
- The square root of 116 is [tex]\(\sqrt{116} \approx 10.770329614269007\)[/tex].
- Multiplying this by 2:
[tex]\[
2 \sqrt{116} \approx 2 \times 10.770329614269007 \approx 21.540659228538015
\][/tex]
Now, we multiply these results together:
[tex]\[
5.656854249492381 \times 2.8284271247461903 \times 21.540659228538015
\][/tex]
The multiplication of these three values gives us the result:
[tex]\[
5.656854249492381 \times 2.8284271247461903 \times 21.540659228538015 \approx 344.6505476566083
\][/tex]
Therefore, the final result of
[tex]\[ 2 \sqrt{8} \times \sqrt{8} \times 2 \sqrt{116} \][/tex]
is approximately
[tex]\[ 344.6505476566083 \][/tex].
