Let's break down the expression [tex]\(\sqrt{3} \cdot 2 + \frac{6}{\sqrt{2}}\)[/tex] step by step to determine its numerical value.
1. Calculate the first term: [tex]\(\sqrt{3} \cdot 2\)[/tex]
- To find the value of this term, you first need to calculate the square root of 3.
- Multiply the result by 2.
The value of [tex]\(\sqrt{3} \cdot 2\)[/tex] is approximately [tex]\(3.4641016151377544\)[/tex].
2. Calculate the second term: [tex]\(\frac{6}{\sqrt{2}}\)[/tex]
- To find the value of this term, you first need to calculate the square root of 2.
- Divide 6 by the result.
The value of [tex]\(\frac{6}{\sqrt{2}}\)[/tex] is approximately [tex]\(4.242640687119285\)[/tex].
3. Add the results of the two terms together:
[tex]\[
3.4641016151377544 + 4.242640687119285
\][/tex]
When you add these two values, the sum is approximately [tex]\(7.70674230225704\)[/tex].
Thus, the value of the expression [tex]\(\sqrt{3} \cdot 2 + \frac{6}{\sqrt{2}}\)[/tex] is approximately [tex]\(7.70674230225704\)[/tex].
