To determine the value of [tex]\(\sqrt{19 + 8\sqrt{3}}\)[/tex], we will follow these steps:
1. Identify the Inner Expression:
We need to find the value of the inner expression [tex]\(19 + 8\sqrt{3}\)[/tex].
2. Find the Value of the Inner Expression:
Evaluate the value of the expression within the square root:
[tex]\[\text{inner expression} = 19 + 8\sqrt{3}\][/tex]
3. Apply the Square Root:
We then take the square root of the evaluated expression to find the final value:
[tex]\[\sqrt{19 + 8\sqrt{3}}\][/tex]
After calculating these steps, we find the value of the expression inside the square root and then obtain the square root value.
The value of [tex]\(\sqrt{19 + 8\sqrt{3}}\)[/tex] is approximately:
[tex]\[
5.732050807568877
\][/tex]
