Let's evaluate the given expression [tex]$\sqrt{a^2 + 12} + |b|$[/tex] step-by-step when [tex]\(a = -2\)[/tex] and [tex]\(b = 14\)[/tex].
1. Square of [tex]\(a\)[/tex]:
[tex]\[
a^2 = (-2)^2 = 4
\][/tex]
2. Inside the square root calculation:
[tex]\[
a^2 + 12 = 4 + 12 = 16
\][/tex]
3. Square root calculation:
[tex]\[
\sqrt{16} = 4
\][/tex]
4. Absolute value of [tex]\(b\)[/tex]:
[tex]\[
|b| = |14| = 14
\][/tex]
5. Final expression value:
[tex]\[
\sqrt{a^2 + 12} + |b| = 4 + 14 = 18
\][/tex]
Thus, the value of the expression [tex]$\sqrt{a^2 + 12} + |b|$[/tex] when [tex]\(a = -2\)[/tex] and [tex]\(b = 14\)[/tex] is:
[tex]\[
18
\][/tex]
