Sure, let's tackle this step-by-step.
1. Given Expression:
We need to estimate the value of [tex]\(\frac{-2 - \sqrt{15}}{2}\)[/tex].
2. Calculate [tex]\(\sqrt{15}\)[/tex]:
Using a calculator, we find the approximate value of [tex]\(\sqrt{15}\)[/tex].
[tex]\[
\sqrt{15} \approx 3.872
\][/tex]
3. Substitute [tex]\(\sqrt{15}\)[/tex] in the Expression:
Substitute the estimated value of [tex]\(\sqrt{15}\)[/tex] into the given expression.
[tex]\[
\frac{-2 - 3.872}{2}
\][/tex]
4. Simplify the Numerator:
Add [tex]\(-2\)[/tex] and [tex]\(-3.872\)[/tex] in the numerator.
[tex]\[
-2 - 3.872 = -5.872
\][/tex]
5. Divide by the Denominator:
Divide [tex]\(-5.872\)[/tex] by 2.
[tex]\[
\frac{-5.872}{2} = -2.936
\][/tex]
6. Round to the Nearest Hundredth:
Round [tex]\(-2.936\)[/tex] to the nearest hundredth.
[tex]\[
-2.936 \approx -2.94
\][/tex]
So the estimated value of [tex]\(\frac{-2 - \sqrt{15}}{2}\)[/tex], rounded to the nearest hundredth, is approximately:
[tex]\[
\boxed{-2.94}
\][/tex]
