Answer :

Certainly! Let's break down the expression [tex]\(\sqrt{3} \cdot 2 + \frac{6}{\sqrt{2}}\)[/tex] step-by-step and find the value:

1. Evaluate [tex]\(\sqrt{3} \cdot 2\)[/tex]:
[tex]\[ \sqrt{3} \cdot 2 \approx 3.4641016151377544 \][/tex]

2. Evaluate [tex]\(\frac{6}{\sqrt{2}}\)[/tex]:
[tex]\[ \frac{6}{\sqrt{2}} \approx 4.242640687119285 \][/tex]

3. Add the two results together:
[tex]\[ \sqrt{3} \cdot 2 + \frac{6}{\sqrt{2}} \approx 3.4641016151377544 + 4.242640687119285 \][/tex]

4. Calculate the sum:
[tex]\[ 3.4641016151377544 + 4.242640687119285 = 7.706742302257039 \][/tex]

Thus, the value of the expression [tex]\(\sqrt{3} \cdot 2 + \frac{6}{\sqrt{2}}\)[/tex] is approximately [tex]\(7.706742302257039\)[/tex].