Select the correct answer.

Estimate the value of [tex]$\frac{\sqrt{2} \pi}{\sqrt{5}}$[/tex]

A. 0.33
B. 0.50
C. 0.67
D. 2.0



Answer :

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