To solve this problem, let's go through it step by step:
1. We are given that [tex]\( a = 2\sqrt{3} \)[/tex].
2. The numeric value of [tex]\( 2\sqrt{3} \)[/tex] is approximately [tex]\( 3.464 \)[/tex].
Looking at the multiple choices provided, let's examine the value of [tex]\( a = 2\sqrt{3} \)[/tex] in the context of these choices:
- [tex]\( \sqrt{3} \)[/tex] is approximately [tex]\( 1.732 \)[/tex].
- Option a): [tex]\( 2 \sqrt{3} \)[/tex], which we've already established is [tex]\( a = 2\sqrt{3} \)[/tex].
- Option b): [tex]\( 2 \)[/tex], which is simply the integer 2.
- Option c): 4, another integer.
- Option d): 6, yet another integer.
If we compare the values derived from the options:
- [tex]\( 2 \sqrt{3} \)[/tex] is approximately [tex]\( 3.464 \)[/tex] which matches the calculated value of [tex]\( a \)[/tex].
Thus, the exact value of [tex]\( b \)[/tex] that corresponds to the given [tex]\( a \)[/tex] must be the same [tex]\( a = 2\sqrt{3} \)[/tex].
Therefore, the value of [tex]\( b \)[/tex] is also [tex]\( 2\sqrt{3} \)[/tex].
