Let's consider the standard and usually used value of irrational numbers given in the question.
- It is asked to see which is closed to 5.66
So, let's see the options:
A) GiveN:
[tex] \dfrac{\pi}{2} + \pi[/tex]
Let consider π = 3.14
[tex] \dfrac{3.14}{2} + 3.14[/tex]
[tex]1.57 + 3.14[/tex]
[tex]4.71 \: (approx.)[/tex]
B) GiveN:
[tex]2\pi - 1[/tex]
Here also, let's consider the value be 3.14
[tex]2 \times 3.14 - 1[/tex]
[tex]6.28 - 1[/tex]
[tex]5.28 \: (approx.)[/tex]
C) GiveN:
[tex]4 \sqrt{2} [/tex]
Let's consider the value of √2 be 1.414
[tex]4 \times 1.414[/tex]
[tex]5.6516 \: (approx.)[/tex]
D) GiveN:
[tex]8 - \sqrt{3} [/tex]
Let's consider the value of √3 be 1.732
[tex]8 - 1.732[/tex]
[tex]6.268 \: (approx.)[/tex]
So, we can see that we have got the approximate value of all the numericals, and the closest to 5.66 is 5.6516 which is the answer of Option C.
So, Correct answer is C
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