To find the value of the given expression [tex]\(\sqrt{a^3-7} + |b|\)[/tex] when [tex]\(a=2\)[/tex] and [tex]\(b=-4\)[/tex], we follow these steps:
1. Calculate [tex]\(a^3 - 7\)[/tex] when [tex]\(a = 2\)[/tex]:
[tex]\[
a^3 = 2^3 = 8
\][/tex]
[tex]\[
a^3 - 7 = 8 - 7 = 1
\][/tex]
2. Take the square root of the result:
[tex]\[
\sqrt{1} = 1.0
\][/tex]
3. Calculate the absolute value of [tex]\(b\)[/tex] when [tex]\(b = -4\)[/tex]:
[tex]\[
|b| = |-4| = 4
\][/tex]
4. Add the two results together:
[tex]\[
1.0 + 4 = 5.0
\][/tex]
Thus, the value of the expression is [tex]\(5.0\)[/tex].
