Sure, let's evaluate the expression [tex]\(\sqrt{a^2 + 12} + |b|\)[/tex] given [tex]\(a = -2\)[/tex] and [tex]\(b = 14\)[/tex].
1. First, calculate the value of [tex]\(a^2 + 12\)[/tex]:
[tex]\[
a^2 = (-2)^2 = 4
\][/tex]
[tex]\[
a^2 + 12 = 4 + 12 = 16
\][/tex]
2. Next, take the square root of this result:
[tex]\[
\sqrt{16} = 4.0
\][/tex]
3. Now, find the absolute value of [tex]\(b\)[/tex]:
[tex]\[
|14| = 14
\][/tex]
4. Finally, add the two results together:
[tex]\[
4.0 + 14 = 18.0
\][/tex]
Therefore, the value of the expression is [tex]\(18.0\)[/tex].
