Let's start by determining the value of [tex]\( x \)[/tex].
1. Given:
[tex]\[
x = 11 + \sqrt{112}
\][/tex]
2. Now, we calculate [tex]\( \sqrt{x} \)[/tex]:
[tex]\[
\sqrt{x} \approx 4.645751311064591
\][/tex]
3. Next, we need to find [tex]\(\frac{3}{\sqrt{x}}\)[/tex]:
[tex]\[
\frac{3}{\sqrt{x}} \approx \frac{3}{4.645751311064591} \approx 0.645751311064591
\][/tex]
4. Add the two values together:
[tex]\[
\sqrt{x} + \frac{3}{\sqrt{x}} \approx 4.645751311064591 + 0.645751311064591 \approx 5.291502622129181
\][/tex]
Therefore, [tex]\(\sqrt{x} + \frac{3}{\sqrt{x}} \)[/tex] is approximately [tex]\( 5.291502622129181 \)[/tex].
