To solve for the product [tex]\( 7 \sqrt{6}(2 \sqrt{10} - 5 \sqrt{2}) \)[/tex], we need to follow these steps:
1. First, calculate the value of each individual term:
- Compute [tex]\( 7 \sqrt{6} \)[/tex]:
[tex]\[
7 \sqrt{6} \approx 17.146428199482244
\][/tex]
2. Next, compute [tex]\( 2 \sqrt{10} - 5 \sqrt{2} \)[/tex]:
- Compute [tex]\( 2 \sqrt{10} \)[/tex]:
[tex]\[
2 \sqrt{10} \approx 6.324555320336759
\][/tex]
- Compute [tex]\( 5 \sqrt{2} \)[/tex]:
[tex]\[
5 \sqrt{2} \approx 7.0710678118654755
\][/tex]
- Subtract the two results:
[tex]\[
2 \sqrt{10} - 5 \sqrt{2} \approx 6.324555320336759 - 7.0710678118654755 \approx -0.7465124915287165
\][/tex]
3. Lastly, multiply the results from steps 1 and 2:
[tex]\[
7 \sqrt{6} \times (2 \sqrt{10} - 5 \sqrt{2}) \approx 17.146428199482244 \times -0.7465124915287165 \approx -12.800022836013733
\][/tex]
Thus, the product [tex]\( 7 \sqrt{6}(2 \sqrt{10} - 5 \sqrt{2}) \)[/tex] is approximately [tex]\(-12.800022836013733\)[/tex].
