Select the correct answer.

Which of these numbers is the most precise approximation of [tex]\sqrt{12}[/tex]?

A. [tex]3.0[/tex]
B. [tex]3.446[/tex]
C. [tex]3.46[/tex]
D. [tex]3.464[/tex]



Answer :

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]