Taking [tex]\(\sqrt{2}=1.414\)[/tex] and [tex]\(\pi=3.141\)[/tex], evaluate [tex]\(\frac{1}{\sqrt{2}} + \pi\)[/tex] up to three decimal places.



Answer :

First, let's start by evaluating the value of [tex]\( \frac{1}{\sqrt{2}} \)[/tex] where [tex]\( \sqrt{2} \)[/tex] is approximately 1.414.

1. Calculate [tex]\( \frac{1}{\sqrt{2}} \)[/tex]:
[tex]\[ \frac{1}{\sqrt{2}} \approx \frac{1}{1.414} \][/tex]
Using division, we get:
[tex]\[ \frac{1}{1.414} \approx 0.707 \][/tex]

2. Add the result to [tex]\( \pi \)[/tex]:
[tex]\( \pi \)[/tex] is given as approximately 3.141.

Now, we need to add these two values:
[tex]\[ 0.707 + 3.141 \][/tex]

3. Perform the addition:
[tex]\[ 0.707 + 3.141 = 3.848 \][/tex]

4. Round the result to three decimal places:
The sum 3.848 is already rounded to three decimal places.

Therefore, the value of [tex]\( \frac{1}{\sqrt{2}} + \pi \)[/tex] up to three decimal places is:

[tex]\[ 3.848 \][/tex]