To find the value of the expression [tex]\( \sqrt{a^2 + 12} + |b| \)[/tex] for [tex]\( a = -2 \)[/tex] and [tex]\( b = 14 \)[/tex], follow these steps:
1. Calculate [tex]\( a^2 + 12 \)[/tex]:
[tex]\[ a = -2 \][/tex]
[tex]\[ a^2 = (-2)^2 = 4 \][/tex]
[tex]\[ a^2 + 12 = 4 + 12 = 16 \][/tex]
2. Calculate [tex]\( \sqrt{a^2 + 12} \)[/tex]:
[tex]\[ \sqrt{16} = 4.0 \][/tex]
3. Calculate the absolute value of [tex]\( b \)[/tex]:
[tex]\[ b = 14 \][/tex]
[tex]\[ |14| = 14 \][/tex]
4. Sum the two parts:
[tex]\[ \sqrt{a^2 + 12} + |b| = 4.0 + 14 = 18.0 \][/tex]
Therefore, the value of the expression is [tex]\( 18.0 \)[/tex].
