Let's find out which of the given options is the closest approximation to the square root of 12.
First, we need to note the value of the square root of 12, [tex]$\sqrt{12}$[/tex].
The square root of 12 is an irrational number that is approximately equal to 3.464.
Given the choices:
A. [tex]\( 3.0 \)[/tex]
B. [tex]\( 3.446 \)[/tex]
C. [tex]\( 3.46 \)[/tex]
D. [tex]\( 3.464 \)[/tex]
We should compare each of these choices to the approximate value of [tex]$\sqrt{12}$[/tex] which is 3.464.
- The option [tex]\( 3.0 \)[/tex] is quite far from 3.464.
- The option [tex]\( 3.446 \)[/tex] is closer, but still a bit off.
- The option [tex]\( 3.46 \)[/tex] is very close, missing only by a small margin of 0.004.
- The option [tex]\( 3.464 \)[/tex] matches exactly with 3.464.
Among these choices, option D. [tex]\( 3.464 \)[/tex] is the most precise approximation of [tex]$\sqrt{12}$[/tex].
Therefore, the correct answer is:
D. [tex]\( 3.464 \)[/tex]
