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].
