To solve the expression [tex]\(\sqrt{a^2 + 12} + |b|\)[/tex] when [tex]\(a = -2\)[/tex] and [tex]\(b = 14\)[/tex], follow these steps:
1. Calculate [tex]\(a^2\)[/tex]:
[tex]\[
a = -2 \implies a^2 = (-2)^2 = 4
\][/tex]
2. Add 12 to [tex]\(a^2\)[/tex]:
[tex]\[
4 + 12 = 16
\][/tex]
3. Calculate the square root:
[tex]\[
\sqrt{16} = 4.0
\][/tex]
4. Calculate the absolute value of [tex]\(b\)[/tex]:
[tex]\[
b = 14 \implies |14| = 14
\][/tex]
5. Add the results together:
[tex]\[
4.0 + 14 = 18.0
\][/tex]
Thus, the value of the expression is [tex]\(\boxed{18.0}\)[/tex].
