Certainly! Let's solve each expression step by step.
1. First Expression: [tex]\(85 \sqrt{12} \times \sqrt{18} - 3 \sqrt{8} \times \sqrt{48}\)[/tex]
Break it down into two parts:
- Calculate [tex]\(85 \sqrt{12} \times \sqrt{18}\)[/tex]
- Calculate [tex]\(3 \sqrt{8} \times \sqrt{48}\)[/tex]
Then subtract the second part from the first part.
The value of this expression is 1190.4520149926245.
2. Second Expression: [tex]\(5 \sqrt{8} + \sqrt{32}\)[/tex]
Break it down into two parts:
- Calculate [tex]\(5 \sqrt{8}\)[/tex]
- Calculate [tex]\(\sqrt{32}\)[/tex]
Then add these two results together.
The value of this expression is 19.79898987322333.
3. Third Expression: [tex]\(2 \sqrt{6} \times 3 \sqrt{8}\)[/tex]
Multiply [tex]\(2 \sqrt{6}\)[/tex] by [tex]\(3 \sqrt{8}\)[/tex].
The value of this expression is 41.569219381653056.
Therefore, the detailed results for each of the given mathematical expressions are:
1. [tex]\(85 \sqrt{12} \times \sqrt{18} - 3 \sqrt{8} \times \sqrt{48} = 1190.4520149926245\)[/tex]
2. [tex]\(5 \sqrt{8} + \sqrt{32} = 19.79898987322333\)[/tex]
3. [tex]\(2 \sqrt{6} \times 3 \sqrt{8} = 41.569219381653056\)[/tex]
These results provide the exact values calculated for each expression.
