Sure, let's carefully work through the problem step by step.
We are asked to estimate the value of the expression:
[tex]\[
\frac{\sqrt{2} \pi}{\sqrt{5}}
\][/tex]
Here are the steps to estimate this value:
1. Evaluate [tex]\(\sqrt{2}\)[/tex]:
The square root of 2 is approximately [tex]\(1.414\)[/tex].
2. Given [tex]\(\pi\)[/tex] (Pi):
The value of [tex]\(\pi\)[/tex] is approximately [tex]\(3.14159\)[/tex].
3. Evaluate [tex]\(\sqrt{5}\)[/tex]:
The square root of 5 is approximately [tex]\(2.236\)[/tex].
4. Calculate the numerator:
[tex]\[
\sqrt{2} \pi \approx 1.414 \times 3.14159 \approx 4.442
\][/tex]
5. Construct the fraction and divide:
[tex]\[
\frac{\sqrt{2} \pi}{\sqrt{5}} \approx \frac{4.442}{2.236} \approx 1.986
\][/tex]
So, the estimated value is around [tex]\(1.986\)[/tex].
Looking at the options, the closest to [tex]\(1.986\)[/tex] is:
D. 2.0
