Answer :
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]
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]
